# Oscillations Questions

We provide oscillations practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on oscillations skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of oscillations Questions

Question NoQuestionsClass
1A small body of mass 10 gram is making harmonic oscillations along a straight line with a time period of ( frac{pi}{4} ) and the maximum displacement is 10 cm. The energy of oscillation is
в. ( 0.16 times 10^{-2} mathrm{J} )
c. ( 0.6 times 10^{-2} J )
D. ( 0.56 times 10^{-2} J )
11
2A particle executing simple harmonic
motion with an amplitude ( 5 mathrm{cm} ) and a
time period 0.2 s. The velocity and acceleration of the particle when the displacement is ( 5 mathrm{cm} ) is
A ( .0 .5 pi m s^{-1}, 0 m s^{-2} )
B. ( 0.5 m s^{-1},-5 pi^{2} m s^{-2} )
C. ( 0 m s^{-1},-5 pi^{2} m s^{-2} )
D. ( 0.5 pi m s^{-1},-0.5 pi^{2} m s^{-2} )
11
3A particle executing SHM has a
maximum speed of ( 30 mathrm{cm} s^{-1} ) and a
maximum acceleration of ( 60 mathrm{cms}^{-2} ). The
period of oscillation is:
A . ( pi )
в. ( frac{pi}{2} s )
c. ( 2 pi )
D. ( frac{2 pi}{15} )
11
4If the time period of a pendulum is ( 25 s )
What is the frequency of the pendulum?
A ( cdot 4 times 10^{-2} mathrm{Hz} )
в. ( 4 times 10^{-1} mathrm{Hz} )
c. ( 25 times 10^{-2} mathrm{Hz} )
D. ( 2 times 10^{-2} mathrm{Hz} )
11
5The time period of oscillation of a particle, that executes SHM, is ( 1.2 s ). The time, starting from mean position, at which its velocity will be half of its velocity at mean position is?
A . ( 0.1 s )
B. ( 0.2 s )
( c .0 .4 s )
D. ( 0.6 s )
11
6The circular motion of a particle with
constant speed is
A. Periodic but not simple harmonic
B. Simple harmonic but not periodic
C. Periodic and simple harmonic
D. Neither periodic nor simple harmonic
11
7Any oscillation in which the amplitude of the oscillating quantity decreases with time is termed as
A. Damped oscillation
B. Free oscillation
c. Depletion oscillation
D. None of these
11
8The mass of particle executing S.H.M is gm.lf its periodic time is ( pi ) seconds,
the value of force constant is:-
A. 4 dynes/cm
B. ( 4 mathrm{N} / mathrm{cm} )
( c cdot 4 N / m )
D. 4 dynes/m
11
9The ratio of time periods of oscillations of situations shown in figures (i) and
(ii) is:
A .2: 3
B. ( 3: sqrt{2} )
( c cdot 4: 3 )
D. 1: 1
11
10For a particle executing SHM having amplitude ‘a’ the speed of the particle is one half of its maximum speed when its displacement from the mean position is
( A cdot a / 2 )
в.
c. ( a frac{sqrt{3}}{2} )
D. 2a
11
11The frequency of a particle performing SHM is 12 Hz. Its amplitude is ( 4 mathrm{cm} ). Its initial displacement is ( 2 mathrm{cm} ) towards positive extreme position. Its equation for displacement is
A. ( x=0.04 cos (24 pi t+pi / 6) )
В. ( x=0.04 sin (24 pi t) )
c. ( x=0.04 sin (24 pi t+pi / 6) )
D. ( x=0.04 cos (24 pi t) )
11
12The displacement of a particle executing SHM at any instant ( t ) is ( x= ) ( 0.01 sin 100(t+0.05) ) then its time
period will be
A . ( 0.06 mathrm{s} )
B. 0.2
c. ( 0.1 mathrm{s} )
D. 0.02
11
13A mass of ( 1 mathrm{kg} ) is suspended from a
spring of force constant ( 400 mathrm{N} ) executing SHM total energy of the body is ( 2 mathrm{J} ), then maximum acceleration of
the spring will be
( mathbf{A} cdot 4 m / s^{2} )
в. ( 40 m / s^{2} )
c. ( 200 m / s^{2} )
D. ( 400 mathrm{m} / mathrm{s}^{2} )
11
14The equilibrium position for a static pendulum changes with
A. acceleration of the bob
B. velocity of the bob
c. displacement of the bob
D. none of the above
11
15State whether true or false.
The S.I. unit of frequency is Hertz (Hz).
A. True
B. False
11
16A particle performing periodic motion satisfies the equation:
( mathbf{A} cdot f(t)=f(t)+T )
B. ( f(t)=f(t)-T )
c. ( f(t)=f(t+T) )
D. None of the above
11
17A particle performs SHM on a straight line with time period ( T ) and amplitude
A. The average speed of the particle between two successive instants, when
potential energy and kinetic energy become same is
A ( cdot frac{A}{T} )
в. ( frac{4 sqrt{2} A}{T} )
c. ( frac{2 A}{T} )
D. ( frac{2 sqrt{2} A}{T} )
11
18The average energy in one time period in simple harmonic motion is.
A ( cdot frac{1}{2} m omega^{2} A^{2} )
B ( cdot frac{1}{4} m omega^{2} A^{2} )
( mathrm{c} cdot m omega^{2} A^{2} )
D. zero
11
19A person drives the paddle ball by moving his finger up and down at a certain frequency. In this example he is causing
A. a damped vibration
B. a forced vibration
c. a mechanical vibration
D. a transnational vinration
11
20A particle executing simple harmonic motion has an angular frequency of ( 6.28 s^{-1} ) and an amplitude of ( 10 mathrm{cm}, ) the speed when the displacement is ( 6 mathrm{cm} ) from the mean position is:
A. ( 50.2 mathrm{cm} / mathrm{s} )
в. ( 60.2 mathrm{cm} / mathrm{s} )
c. ( 70.2 mathrm{cm} / mathrm{s} )
D. ( 80.2 mathrm{cm} / mathrm{s} )
11
21The amplitude of a damped oscillator decreases to 0.9times its original magnitude in 5 s. In another 10 s it will
decrease to ( alpha ) times its original
magnitude, where ( alpha ) equals
A. 0.7
B. 0.81
c. 0.729
D. 0.6
11
22The total energy of a simple harmonic oscillator is proportional to
A. amplitude
B. square of amplitude
c. frequency
D. velocity
11
23A particle of mass ( m ) is located in a unidimensional potential field, where
the potential energy of the particle
depends on the coordinates as ( U(x)= )
( U_{0}(1-sin b x) ; ) where ( U_{0} ) and ( b ) are
constant. find the period of small
oscillations that the particle performs about the equilibrium position.
A ( cdot frac{2 pi}{b^{2}} sqrt{frac{m}{U_{0}}} )
В. ( frac{pi}{b} sqrt{frac{m}{U_{0}}} )
c. ( frac{pi^{2}}{2 b} sqrt{frac{m}{U_{0}}} )
D. ( frac{2 pi}{b} sqrt{frac{m}{U_{0}}} )
11
24In the arrangement shown, the solid cylinder of mass ( mathrm{m} ) is slightly rolled to the left and released. It starts
oscillating on the horizontal surface without slipping. Then time period of oscillation is
( ^{mathrm{A}} cdot pi sqrt{frac{3 K}{m}} )
в. ( 2 pi sqrt{frac{3 M}{2 K}} )
c. ( _{2 pi} sqrt{frac{2 K}{3 M}} )
D. ( 2 pi sqrt{frac{3 K}{2 m}} )
11
25Which of the following functions correctly represent the travelling wave equation for finite values of ( x ) and ( t )
A ( cdot y=x^{2}-t^{2} )
B ( cdot y=cos x^{2} sin t )
c. ( y=log left(x^{2}-t^{2}right)-log (x-t) )
D・ ( y=e^{2 x} sin t )
11
26In damped oscillation mass is 1 kg and
spring constant ( =100 N / m, ) damping
coefficeint ( =0.5 mathrm{kg} s^{-1} . ) If the mass
displaced by ( 10 mathrm{cm} ) from its mean position then what will be the value of
its mechanical energy after 4 seconds?
A . ( 0.67 J )
в. 0.067 Л
c. ( 6.7 J )
D. ( 0.5 J )
11
27A particle executes simple harmonic motion with a frequency f. The frequency with which the kinetic energy oscillates is
( A cdot y / 2 )
B.
( c cdot 2 y )
D. none of these
11
28In which of the following there is some loss of energy in the form of heat
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All
11
29The piston in the cylinder head of a locomotive has a stroke of 6 m. If the
piston executing simple harmonic motion with an angular frequency of
200 rad ( m i n^{-1}, ) its maximum speed is
A ( .5 mathrm{ms}^{-1} )
B . ( 10 mathrm{ms}^{-1} )
c. ( 15 mathrm{ms}^{-1} )
D. ( 20 m s^{-1} )
11
30When a particle executing SHM
oscillates with a frequency ( nu, ) then the
kinetic energy of the particle:
A. changes periodically with a frequency of ( nu )
B. changes periodically with a frequency of ( 2 nu )
C . changes periodically with a frequency of ( frac{nu}{2} )
D. remains constant
11
31Find the torque of a force ( overrightarrow{boldsymbol{F}}=-mathbf{3} hat{mathbf{i}}+ )
( hat{boldsymbol{j}}+boldsymbol{5} widehat{boldsymbol{k}} ) acting at the point ( overrightarrow{boldsymbol{r}}=boldsymbol{7} hat{boldsymbol{i}}+ )
( mathbf{3} widehat{boldsymbol{j}}+widehat{boldsymbol{k}} )
( mathbf{A} cdot 14 hat{i}-38 hat{j}+16 hat{k} )
B . ( 4 hat{i}-4 widehat{j}+6 hat{k} )
c. ( \$ \$-13-16 ) lhat ( {k}-38 ) lhat ( {j}-16 mid ) hat ( {i} \$ \$ )
D. none of these
11
32A particle executing SHM has amplitude of ( 4 mathrm{cm} ., ) and its acceleration at a distance of ( 1 mathrm{cm} ) from the mean
position is ( 3 mathrm{cm} s^{-2} . ) Its velocity be when it is at a distance of ( 2 mathrm{cm} ) from its mean
position is
A. ( 2 c m / s )
в. ( 3 mathrm{cm} / mathrm{s} )
c. ( 4 c m / s )
D. ( 6 mathrm{cm} / mathrm{s} )
11
33For a particle executing simple harmone motion, the kinetic energy k is
given by ( k=k_{0} cos ^{2} omega t . ) The maximum
value of potential energy is?
( A cdot k_{0} )
B. zero
( c cdot k_{0} / 2 )
D. not obtainable
11
34A body is lying on a piston which is executing vertical SHM. Its time period is 2 s. For what value of amplitude, the
body will leave the piston:
( A cdot 1 m )
B. 0.248 m
c. ( 0.428 mathrm{m} )
D. ( 0.842 mathrm{m} )
11
35Acceleration-time graph of a particle
executing SHM is as shown in the
figure. Select the correct alternative(s)
This question has multiple correct options
A. Displacement of particle at 1 is negative
B. Velocity of particle at 2 is positive
C. Potential energy of particle at 3 is maximum
D. Speed of particle at 4 is decreasing
11
36In a non harmonic motion;
A. Displacement and amplitude are independent of each other
B. Displacement and amplitude are dependent on each other
C . restoring force is proportional to displacement
D. restoring force is zero
11
37Consider a spring that exerts the following restoring force: ( boldsymbol{F}=-boldsymbol{k} boldsymbol{x} ) for
( boldsymbol{x}>0 ) and ( boldsymbol{F}=-4 boldsymbol{k} boldsymbol{x} ) for ( boldsymbol{x}<mathbf{0} )
A mass m on a frictionless surface is
attached to the spring, displaced to ( x=A ) by stretching the spring and then
releasing:
This question has multiple correct options
A cdot The period of motion will be ( T=frac{3}{2} pi sqrt{frac{m}{k}} )
B. The most negative value, the mass ( m ) can reach will be ( x=-frac{A}{2} )
c. The time taken to move from ( x=A ) to ( x=-frac{A}{sqrt{2}} ) straight away will be equal to ( frac{5 pi}{8} sqrt{frac{m}{k}} )
D. The total energy of oscillations will be ( frac{5}{2} k A^{2} )
11
38A particle in S.H.M. has a period of 2
seconds and amplitude of ( 10 mathrm{cm} ) Calculate the acceleration when it is at
( 4 c m ) from its positive extreme position.
11
39A particle executes simple harmonic
motion with an amplitude of ( 4 mathrm{cm} . ) At the mean position the velocity of the particle is ( 10 mathrm{cm} / mathrm{s} ). The distance of the particle from the mean position when its speed becomes ( 5 mathrm{cm} / mathrm{s} ) is
A ( cdot sqrt{3} mathrm{cm} )
B. ( sqrt{5} mathrm{cm} )
c. ( pm 2(sqrt{3}) ) cm
D. ( 2(sqrt{5}) mathrm{cm} )
11
40Statement 1: In simple harmonic motion, the velocity is maximum when the acceleration is minimum.

Statement 2: Displacement and velocity of ( S . H . M ) differ in phase by ( frac{pi}{2} )
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
c. statement 1 is true, statement 2 is true; Statement 2 is not the correct explanation for Statement 1
D. Statement 1 is true, Statement 2 is false

11
41A plank with a body of mass ( m ) placed
on it starts moving straight up
according to the law ( y=a(1-cos omega t) )
where ( y ) is the displacement from the
initial position, ( omega=11 ) rad/s. What is
the force that the body exerts on the
plank?
11
42Vertical displacement of a plank with a
body of mass ‘ ( m ) ‘ on it is varying
according to law ( boldsymbol{y}=sin (boldsymbol{omega} boldsymbol{t})+ )
( sqrt{3} cos (omega t) . ) The minimum value of ( omega ) for
which the mass just breaks off the plank and the moment this occurs first
( operatorname{after} t=0 ) are given by ( (y ) is positive
vertically upwards):
A ( cdot sqrt{frac{g}{2}}, sqrt{frac{2}{g}} frac{pi}{6} )
В ( cdot frac{g}{sqrt{2}} frac{2}{3}, sqrt{frac{pi}{g}} )
c. ( sqrt{frac{g}{2}} frac{pi}{3}, sqrt{frac{2}{g}} )
D. ( sqrt{2 g}, sqrt{frac{2 pi}{3 g}} )
11
43A particle performing SHM takes time equal to T (time period of SHM) in
consecutive appearances at a
particular point. This point is
A. An extreme position
B. The mean position
C. Between positive extreme and mean position
D. Between negative extreme and mean position
11
44A body of mass ( 0.1 k g ) is executing simple harmonic motion according to the equation ( boldsymbol{x}=mathbf{0 . 5} cos left(mathbf{1 0 0} boldsymbol{t}+frac{mathbf{3} boldsymbol{pi}}{mathbf{4}}right) ) metre. Find:
(i) the frequency of oscillation, (ii)
initial phase, (iii) maximum velocity,
(iv) maximum acceleration,
(v) total
energy.
11
45A particle executes S.H.M with a period of 6 seconds. If the maximum speed is ( 3.14 mathrm{cm} / mathrm{sec}, ) then what is its amplitude?
A. ( 3 mathrm{cm} )
B. ( 5 mathrm{cm} )
( c cdot 6 mathrm{cm} )
D. ( 9 mathrm{cm} )
11
46A simple harmonic motion along the ( x- )
axis has the following properties:
amplitude ( =0.5 m, ) the time to go from
one extreme position to other is, 2 s and
( boldsymbol{x}=mathbf{0 . 3} boldsymbol{m} ) at ( boldsymbol{t}=mathbf{0 . 5} boldsymbol{s} . ) The general
equation of the simple harmonic
motion is
A ( cdot x=(0.5 m) sin left[frac{pi t}{2}+8^{circ}right] )
B. ( x=(0.5 m) sin left[frac{pi t}{2}-8^{circ}right] )
( mathbf{c} cdot_{x}=(0.5 m) cos left[frac{pi t}{2}+8^{circ}right] )
D. ( x=(0.5 m) cos left[frac{pi t}{2}-8^{circ}right] )
11
47A small block oscillates back and forth
on a smooth concave surface of radius
( boldsymbol{R} ). The time period of small oscillation
of the block is :
( ^{mathbf{A}} cdot T=2 pi sqrt{frac{R}{g}} )
В ( cdot T=2 pi sqrt{frac{2 R}{g}} )
c. ( T=2 pi sqrt{frac{R}{2 g}} )
D. none of these
11
48A particle of mass ( m ) is allowed to
oscillate on a smooth parabola: ( boldsymbol{x}^{2}= )
( 4 a y, a>1 ) as shown in the figure. The
angular frequency ( (omega) ) of small
oscillations is
A ( cdot omega=sqrt{frac{g}{4 a}} )
B. ( omega=sqrt{frac{g}{2 a}} )
c. ( omega=sqrt{frac{2 g}{a}} )
( omega=sqrt{frac{g}{a}} )
11
49The variation in potential energy of a
harmonic oscillator is as shown in the
figure. The spring constant is
A ( cdot 1 times 10^{2} mathrm{Nm}^{-1} )
B. ( 1.5 times 10^{2} N m^{-1} )
c. ( 0.0667 times 10^{2} N m^{-1} )
D. ( 3 times 10^{2} mathrm{Nm}^{-} )
11
50The tension of a stretched string is increases by ( 44 % ). In order to keep its frequency of vibration same its length must be increased by.
A . ( 10 % )
B. 20%
c. ( 15 % )
D. ( 25 % )
11
51Figure shows a small magnetised
needle ( P ) placed at a point ( O . ) The arrow
shows the direction of its magnetic
moment. The other arrows show
different positions (and orientations of
the magnetic moment) of another
identical magnetised needle ( Q )
In which configuration the system is not in equilibrium?
11
52A small block oscillates back and forth
on a smooth concave surface of radius
R. Find the time period of small oscillations.
A ( cdot pi sqrt{frac{2 R}{g}} )
в. ( 2 pi sqrt{frac{R}{3 g}} )
c. ( 2 pi sqrt{frac{2 R}{3 g}} )
D. ( 2 pi sqrt{frac{R}{g}} )
11
53Which of the following characteristics
must remain constant for undamped oscillations of the particle?
A. acceleration
B. phase
c. amplitude
D. velocity
11
54A wedge of mass ( m ), having a smooth
semi circular part of radius R is resting on smooth horizontal surface.Now a
particle of mass ( m / 2 ) is released from
the top point of the semicircular part.
Then
This question has multiple correct options
A. The maximum displacement of the wedge will be R
B. The maximum displacement of the wedge will be ( frac{2 R}{3} )
c. The wedge will perform simple harmonic motion of amplitude
D. The wedge will perform oscillatory motion of amplitude ( frac{R}{3} )
11
55The masses in figure slide on a
frictionless table. ( m_{1} ) but not ( m_{2}, ) is
fastened to the spring. If now ( m_{1} ) and
( m_{2} ) are pushed to the left, so that the
spring is compressed a distance ( mathrm{d} ) what will be the amplitude of the
oscillation of ( m_{1} ) after the spring
system is released?
( ^{mathrm{A}} cdot_{A}=(sqrt{frac{m_{1}}{m_{1}+m_{2}}}) )
B. ( A=(sqrt{frac{m_{2}}{m_{1}+m_{2}}}) d )
( ^{mathbf{c}} cdot_{A}=(sqrt{frac{m_{1}}{m_{1}+m_{2}}}) d )
D. None
11
56Function ( boldsymbol{x}=boldsymbol{A} sin ^{2} boldsymbol{omega} boldsymbol{t}+boldsymbol{B} cos ^{2} boldsymbol{omega} boldsymbol{t}+ )
( C sin omega t cos omega t ) represents SHM
A. For any value of ( A, B ) and ( C ) (except ( C=0 ) )
B. ( A=-B, C=2 B, ) amplitude ( =mid B sqrt{2} )
c. ( A=B ; C=0 )
D. ( A=B ; C=2 B, ) amplitude ( =|B| )
11
57A particle moves along the ( x ) -axis
according to: ( boldsymbol{x}=boldsymbol{A}[mathbf{1}+boldsymbol{s} boldsymbol{i} boldsymbol{n} boldsymbol{omega} boldsymbol{t}] . ) What
distance does it travel between ( t=0 ) and
( boldsymbol{t}=mathbf{2 . 5} boldsymbol{pi} / boldsymbol{omega} ? )
A. ( 4 A )
B. 6A
( c cdot 5 A )
D. None
11
58A thin fixed ring of radius ( 1 mathrm{m} ) has a positive charge ( 1 times 10^{-5} mathrm{C} ) uniformly
distributed over it. A particle of mass ( 0.9 mathrm{g} ) and having a negative charge of
( 1 times 10^{-6} mathrm{C} ) is placed on the axis at a
distance of ( 1 mathrm{cm} ) from the centre of the ring. Calculate the time period of oscillations.
A . 0.5 secs
B. 9.28 secs
c. 0.628 secs
D. 0.1 secs
11
59A force ( F=-4 x-8 ) is acting on a block where ( x ) is position of block in meter The energy of oscillation is 32 J, the block oscillate between two points Position of extreme position is:
( A cdot 6 )
B. 0
( c cdot 4 )
D. 3
11
60If two SHMs of different amplitudes are added together, the resultant SHM will be a maximum if the phase difference between them is
( mathbf{A} cdot pi / 2 )
в. ( pi / 4 )
( c )
D. ( 2 pi )
11
61A body is executing S.H.M. When its displacement from the mean position is ( 4 mathrm{cm} ) and ( 5 mathrm{cm}, ) the corresponding
velocity of the body is ( 10 mathrm{cm} / mathrm{sec} ) and 8 ( mathrm{cm} / mathrm{sec} . ) Then the time period of the body is:
A ( .2 pi sec )
B . ( pi / 2 ) sec
( c . pi mathrm{sec} )
D. 3pi/2 sec
11
62In an SHM, restoring force is ( boldsymbol{F}=-boldsymbol{k} boldsymbol{x} )
where ( k ) is force constant, ( x ) is
displacement and ( A ) is the amplitude of motion, then the total energy depends
upon
A. ( k, A ) and ( M )
в. ( k, x, M )
( c cdot k, A )
D. ( k, x )
11
63A highly rigid cubical block A of smal mass M and side L is fixed rigidly onto another cubical block B of same
dimensions and of low modulus of
rigidly ( eta ) such that lower face of ( A ) completely covers the upper face of B. The lower face of B is rigidly held on a horizontal surface. A small force is
applied perpendicular to one the side face of A. After the force is withdrawn, block A executes small oscillations, the
time period of which is given by
в. ( 2 pi sqrt{frac{M}{eta L}} )
c. ( 2 pi sqrt{frac{M L}{eta}} )
D. ( sqrt{frac{M eta}{L}} )
11
64A particle is executing SHM with amplitude ( A ) and has maximum velocity
( V_{0} . ) Find its speed when it is located at
distance of A/2 from mean position.
11
65Which of the following quantities are always negative?
A ( cdot vec{F} cdot vec{r} )
в. ( vec{v} cdot vec{r} )
c. ( vec{a} cdot vec{r} )
D. Both ( A ) and ( C )
11
66At ( t=0, ) the displacement of a particle
in S.H.M. is half its amplitude. Its initial phase is:
A ( cdot frac{pi}{6} ) rad
B ( cdot frac{pi}{3} ) rad
c. ( frac{2 pi}{3} ) rad
11
67If density (D) acceleration (a) and force
(F) are taken as basic quantities,then Time period has dimensions
A ( cdot frac{1}{6} ) in ( F )
B. ( -frac{1}{6} ) in ( F )
( c cdot-frac{2}{3} ) in ( F )
D. All the above are true
11
68Phase different between the
instantaneous velocity and acceleration of particle executing SHM is
A . zero
в. ( frac{pi}{2} )
( c . pi )
D. ( 2 pi )
11
69A horizontal platform with an object placed on it is executing simple harmonic motion in the vertical
direction. The amplitude of oscillation is ( 3.92 times 10^{-3} ) m. What should be the
least period of these oscillations, so that the object is not detached from the
platform?
A. 0.145 sec
B. 0.1556 sec
c. ( 0.1256 mathrm{sec} )
D. ( 0.1356 mathrm{sec} )
11
70The amplitude and the time period in a
S.H.M. is ( 0.5 mathrm{cm} ) and 0.4 see respectively If the initial phase is ( r / 2 ) radiam,then the equaction of S.H.H. will be
A ( cdot y=0.5 sin 5 / pi )
B. ( y=0.5 sin 4 / pi )
c. ( y=0.5 sin 2.5 / pi )
D. ( y=0.5 cos 5 pi t )
11
71Which of the following functions of time represent ( (A) ) simple harmonic, ( (B) ) periodic but not simple harmonic, and
( (C) ) non-periodic motion? Give period for each case of periodic motion ( (omega ) is any positive constant):
(a) ( sin omega t-cos omega t )
( (b) sin ^{3} omega t )
(c) ( 3 cos (pi / 4-2 omega t) )
( (d) cos omega t+cos 3 omega t+cos 5 omega t )
( (e) exp left(-omega^{2} t^{2}right) )
(f) ( 1+omega t+omega^{2} t^{2} )
11
72A plot of displacement of a particle with
time is as shown in the figure. The
equation of SHM is
A ( . x= ) Asinwt
B. ( x= ) Acoswt
c. ( x=- ) Acoswt
D. ( x=- ) Asinwt
11
73A point mass oscillates along the ( x ) axis according to the law ( boldsymbol{x}= )
( x_{0} cos (omega t-pi / 4) . ) If the acceleration of
the particle is written as ( a= )
( A cos (omega t+delta) ) then:
A ( . A=x_{0}, delta=-pi / 4 )
B . ( A=x_{0} omega^{2}, delta=-pi / 4 )
C ( . A=x_{0} omega^{2}, delta=-pi / 8 )
D. ( A=x_{0} omega^{2}, delta=3 pi / 4 )
11
74Average kinetic energy in one time
period of a simple harmonic oscillator whose amplitude is ( A, ) angular velocity ( omega ) and mass ( m, ) is
A ( cdot frac{1}{4} m omega^{2} A^{2} )
B ( cdot frac{1}{2} m omega^{2} A^{2} )
( mathrm{c} cdot m omega^{2} A^{2} )
D. Zero
11
75A particle is moving with a constant acceleration. Its velocity is reduced to zero in 5 s and it covered a distance of
( 100 mathrm{m} ) in this direction. The distance covered by the particle in the next 5 s is
A. Zero
B. 250 m
c. ( 100 mathrm{m} )
D. 500 ( mathrm{m} )
11
76The equation ( x=a sin 2 t+b cos 2 t ) will
represent an SHM
A. True
B. False
11
77A simple harmonic oscillator has an
acceleration of ( 1.25 mathrm{m} / mathrm{s}^{2} ) at ( 5 mathrm{cm} ) from
the equilibrium. Its period of oscillation is:
A ( frac{4 pi}{5} ) s
в. ( frac{5 pi}{2} ) s
c. ( frac{2 pi}{5} ) s
D. ( frac{2 pi}{25} ) s
11
length ( 4.9 mathrm{m} ). The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The
block is stretched by ( 0.2 mathrm{m} ) and released from rest at ( t=0 . ) It then executes simple
harmonic motion with angular
frequency ( omega=frac{pi}{3} r a d / s )
Simultaneously at ( t=0, ) a small pebble is projected with speed v from point ( mathrm{P} ) at an angle of 45 as shown in the figure. Point ( P ) is at a horizontal distance of 10
( mathrm{m} ) from ( 0 . ) If the pebble hits the block at ( t=1 mathrm{s}, ) the value of ( mathrm{v} ) is
( left(operatorname{take} g=10 m / s^{2}right) )
( mathbf{A} cdot sqrt{50} m / s )
B. ( sqrt{51} mathrm{m} / mathrm{s} )
c. ( sqrt{52} mathrm{m} / mathrm{s} )
D. ( sqrt{53} mathrm{m} / mathrm{s} )
11
79A particle executes SHM given by the equation ( boldsymbol{x}=mathbf{4} sin (mathbf{2} boldsymbol{pi} boldsymbol{t}+boldsymbol{pi} / mathbf{4}), ) what
will be the velocity of the particle at ( t= ) (1/8)th sec;
A. velocity = 0
B. velocity = maximum
c. velocity = minimum
D. The particle’s speed cannot be determined
11
80A simple harmonic oscillator is of mass ( 0.100 mathrm{kg} . ) It is oscillating with a frequency of ( frac{5}{pi} mathrm{Hz} ). If its amplitude of
vibration is ( 5 mathrm{cm}, ) the force acting on the particle at its extreme position is
A. 2 N
B. 1.5 N
( c cdot 1 mathrm{N} )
D. 0.5 N
11
81The maximum kinetic energy of a particle of mass 100 g and time period lpi secs, executing SHM at its mean position is given as 50 J. The amplitude of oscillation is
A ( . A=50 sqrt{10} mathrm{m} )
В. ( A=5 sqrt{10} m )
c. ( A=50 m )
D. ( A=25 m )
11
82Assertion: In forced oscillations, the
steady state motion of the particle is simple harmonic. Reason : Then the frequency of particle after the free oscillations die out, is the
natural frequency of the particle.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
11
83The period of a particle in linear SHM is
8 s. ( A t t=0 ) it is at the mean position. Find the ratio of distance traveled by it
in 1 st second and 2 nd second
A . 3.2:
B. 2.4:
c. 1.6:
D. 4.2:
11
84The velocity of a sound wave in ( v ) and
the wave energy density is ( E, ) then the
amount of energy transferred per unit area per second by the wave in a direction normal to the wave
propagation is
A. ( E )
в. ( E v )
( mathrm{c} cdot E^{2} v^{2} )
D. ( sqrt{E v} )
11
85The potential energy of a particle executing SHM varies sinusoidally with frequency f. The frequency of oscillation of the particle will be:
( A cdot frac{f}{2} )
в. ( frac{f}{sqrt{2}} )
( c cdot f )
D. ( 2 f )
11
86Potential Energy(U) of a body of unit mass moving in a one-dimension conservative force field is given by ( U= )
( left(x^{2}-4 x+3right) . ) All units are in S.I.
(i) Find the equilibrium positions of the body
(ii) Show that oscillations of the body
(iii) Find the amplitude of oscillations if speed of the body at equilibrium position is ( 2 sqrt{6} mathrm{m} / mathrm{s} )
11
87Assertion
There is no difference in the graphs of momentum an velocity of a body performing SHM.
Reason
Momentum is proportional to velocity of
a body.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect and Reason are incorrect
11
88An object swinging on the end of a string forms a simple pendulum. Some students (and some texts) often cite the
simple pendulum’s motion as an example of SHM. That is not quite accurate because the motion is really
A. approximately SHM only for small amplitudes
B. exactly SHM only for amplitudes that are smaller than a certain value
c. approximately SHM for all amplitudes.
D. None of the above
11
89A particle moves in ( x ) -y plane according to the equation ( vec{r}=(hat{i}+hat{j})(A sin omega t+B )
( cos omega t) . ) Motion of the particle is:
A. periodic
в. sнм
c. along a straight line
D. along an ellipse
11
90A particle is executing simple harmonic motion (SHM) of amplitude ( A ), along the ( x ) -axis, about ( x=0 . ) When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be :
A ( cdot frac{A}{2} )
в. ( frac{A}{2 sqrt{2}} )
c. ( frac{A}{sqrt{2}} )
D.
11
91A block is kept on a horizontal table.The table is undergoing simple harmonic motion of frequency ( 3 H z ) in a
horizontal plane.The coefficient of static friction between block and the table
surface is ( 0.72 . ) Find the maximum
amplitude (in ( mathrm{cm} ) ) of the table at which the block does not slip on the surface. ( Take ( left.g=10 m / s^{2} text { and } pi^{2}=10right) )
11
92Two bodies ( mathrm{M} ) and ( mathrm{N} ) of equal mass are suspended from two separate massless
spring of force constant ( k_{1} ) and ( k_{2} )
respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of ( mathrm{M} ) to that of ( mathrm{N} ) is?
( mathbf{A} cdot frac{k_{1}}{k_{2}} )
В. ( sqrt{frac{k_{1}}{k_{2}}} )
( mathbf{c} cdot frac{k_{2}}{k_{1}} )
D. ( sqrt{frac{k_{2}}{k_{1}}} )
11
93The displacement of an object attached to a spring and executing simple harmonic motion is given by ( boldsymbol{x}=mathbf{2} times )
( 10^{-2} ) cos ( pi t ) meters. The time at which
the maximum speed first occurs is :
A . ( 0.5 mathrm{s} )
B. 0.75 s
c. 0.125 s
D. ( 0.25 mathrm{s} )
11
94A particle of mass m free to move in the x-y plane is subjected to a force whose
components are ( boldsymbol{F}_{boldsymbol{x}}=-boldsymbol{k} boldsymbol{y} ) and ( boldsymbol{F}_{boldsymbol{y}}= )
( -k y, ) where ( k ) is a constant. The particle
is released when ( t=0 ) at the point (2,3) Prove that the subsequent motion is simple harmonic along the straight line
( 2 y-3 x=0 )
11
95Which of the following statements is/are correct
(i) The distance between two consecutive compressions is called frequency of sound wave
(ii) Sound propagates as pressure variations
(iii) Compressions are narrower in a high pitched sound
( A cdot( ) i) only
B . (ii) only
c. (iii) only
D. (ii) and (iii)
11
96The tendency of one object to force another adjoining or interconnected object into vibration motion is referred
to as a
A. forced vibration
B. damped vibration
c. loudness
D. pitch
11
97The differential equation representing the SHM of a particule is ( frac{mathbf{9} d^{2} boldsymbol{y}}{d t^{2}}+mathbf{4} boldsymbol{y}= )
0. The time period of the particle is
given by :
A ( cdot frac{pi}{3} ) sec
B . ( pi ) sec
c. ( frac{2 pi}{3} ) sec
D. ( 3 pi ) sec
11
98A particle is executing S.H.M with a frequency ‘f’, the frequency with which is K.E. oscillates is?
( mathbf{A} cdot mathbf{f} )
B. ( f / 2 )
c. ( 2 f )
D. ( 4 f )
11
99A highly rigid cubical block A of small mass ( mathrm{M} ) and side ( mathrm{L} ) is fixed rigidly on to
another cubical block ( mathrm{B} ) of the same
dimensions and of low modulus of
rigidity ( eta ) such that the lower face of ( A )
completely covers the upper face of B. The lower face of B is rigidly held on a
horizontal surface. A small force F is
applied perpendicular to one of a sides faces of A. After the force is withdrawn, block A executes small oscillations, the
time period of which is given by
( mathbf{A} cdot 2 pi sqrt{M eta L} )
в. ( 2 pi sqrt{M eta / L} )
c. ( 2 pi sqrt{M L / eta} )
D. ( 2 pi sqrt{M / eta L} )
11
100In SHM, select the wrong statement, where ( F ) is the force, ( a ) is the
acceleration and ( v ) is the velocity of the
particle in SHM.
A ( cdot vec{F} times vec{v} ) is a null vector
В . ( |vec{F} times vec{a}|=0 ) (always)
c. ( vec{F} times vec{a}<0 )
D. ( vec{a} cdot vec{x}<0 )
11
101The periodic time of a body executing SHM is ( 4 s ). After how much interval from
time ( t=0, ) its displacement will be half
of its amplitude?
A . ( 1 / 2 s )
B. ( 1 / 3 s )
c. ( 1 / 4 s )
D. ( 1 / 6 s )
11
102The coefficient of friction between two
blocks of masses ( 1 mathrm{kg} ) and ( 4 mathrm{kg} ) as
shown in figure is ( mu ) and the horizontal
plane is smooth. If the system is slightly displaced and released it will execute
S.H.M. The maximum amplitude if the
upper block does not slip relative to lower block will be (k is spring constant)
( A cdot frac{5 mu g}{k} )
в. ( frac{mu g}{k} )
( c cdot frac{3 mu g}{k} )
D. ( frac{2 mu g}{k} )
11
103For the block under SHM shown in the
figure, which of the following quantities
is not constant?
vertica
oscillation
A. Amplitude
B. Frequency
c. Period
D. Position of block
E. Total mechanical energy of the block
11
104The differential equation for a particle of mass ( 2 mathrm{kg} ) executing ( mathrm{SHM} ) is ( 2 frac{d^{2} x}{d t^{2}}+ )
( x=0 . ) If amplitude of oscillation is 3
( mathrm{cm}, ) then maximum velocity of the particle will be
A. ( 3 sqrt{0.5} mathrm{cm} / mathrm{s} )
B. ( sqrt{0.5} mathrm{cm} / mathrm{s} )
c. ( sqrt{0.5} / 3 mathrm{cm} / mathrm{s} )
D. ( 2 sqrt{0.5} mathrm{cm} / mathrm{s} )
11
105The equation of motion of particle is
given by dp ( / mathrm{dt}+mathrm{m} omega^{2} mathrm{y}=0 ) where p is momentum and y is its position. Then the particle :
A. moves along a straight line
B. moves along a parabola
c. executes simple harmonic motion
D. falls freely under gravity
11
106A paricle executes SHM with time period of 4 s. find the minimum time interval in which the velocity of the particle changes by an amount equal to its maximum velocity:
A ( cdot frac{1}{2} s )
B. ( frac{2}{3} ) s
c. ( frac{9}{3} ) s
D. ( frac{5}{3} ) s
11
107Assertion (A): In damped vibrations, amplitude of oscillation decreases Reason (R): Damped vibrations indicate
loss of energy due to air resistance
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
C. A is true and ( R ) is false
D. A is false and R is true
11
108A system is oscillating with undamped simple harmonic motion.Then the
This question has multiple correct options
A. average total energy per cycle of the motion is its maximum kinetic energy
B. average total energy per cycle of the motion is ( frac{1}{sqrt{2}} )
times its maximum kinetic energy
C root mean square velocity is ( frac{1}{sqrt{2}} ) times its maximum
velocity
D. mean velocity is ( frac{1}{2} ) of maximum velocity
11
109thingy hanging from a spring. The system was set vibrating by pulling the
thingy down below its equilibrium position and then letting it go from
rest. If the initial displacement is
doubled what happens to the maximum
kinetic energy of the thing?
A. It is unchanged.
B. It is doubled
c. It is increased by a factor of ( 4 . )
D. We can’t tell from the information provided
11
110A simple harmonic motion has an amplitude ( A ) and time period ( T . ) Find the time required by it to travel directly from ( boldsymbol{x}=-frac{boldsymbol{A}}{sqrt{mathbf{2}}}, ) to ( boldsymbol{x}=frac{boldsymbol{A}}{sqrt{mathbf{2}}} )11
111All oscillatory motions are
A. periodic
B. linear
c. rotatory
D. curvilinear
11
112Three simple harmonic motions in the
same direction having the same amplitude a and same period are superposed. If each differs in phase
from the next by ( 45^{circ}, ) then :
This question has multiple correct options
A. The resultant amplitude is ( (1+sqrt{2}) a )
B. The phase of the resultant motion relative to the first is ( 90^{circ} )
c. The energy associated with the resulting motion is ( (3+2 sqrt{2}) ) times the energy associated with any single motion
D. The resulting motion is not simple harmonic
11
113A particle of mass ( M ) is executing oscillations about the origin on the ( x )
axis. Its potential energy is ( |boldsymbol{U}|=boldsymbol{K}left|boldsymbol{x}^{2}right| )
where ( K ) is a positive constant. If the
amplitude of oscillations is ( a ), then its
period ( boldsymbol{T} ) is
A. proportional to ( 1 / sqrt{a} )
B. independent of ( a )
c. proportional to ( sqrt{a} )
D. proportional to ( a^{1 / 2} / 2 ) poorional
11
114The maximum acceleration of a particle
in SHM is made two times keeping the
maximum speed to be constant. It is possible when
A. amplitude of oscillation is doubled while frequency remains constant
B. amplitude is doubled while frequency is halved
c. frequency is doubled while amplitude is halved
D. frequency is doubled while amplitude remains constant
11
115In periodic motion, the displacement is
A. directly proportional to the restoring force
B. inversely proportional to the restoring force
c. independent of restoring force
D. independent of any force acting on the particle
11
116A particle with restoring force proportional to displacement and resisting force proportional to velocity
is subjected to a force ( boldsymbol{F} ) sinw. If the
amplitude of the particle is maximum
for ( omega=omega_{1} ) and the energy of the particle
is maximum for ( omega=omega_{2} ) then (where ( omega_{0} )
natural frequency of oscillation of particle)
( mathbf{A} cdot omega_{1}=omega_{0} ) and ( omega_{2} neq omega_{0} )
B . ( omega_{1}=omega_{0} ) and ( omega_{2}=omega_{0} )
C ( cdot omega_{1} neq omega_{0} ) and ( omega_{2}=omega_{0} )
D. ( omega_{1} neq omega_{0} ) and ( omega_{2} neq omega_{0} )
11
117A body of mass ( mathrm{M} ) is situated in a
potential field ( boldsymbol{U}(boldsymbol{x})=boldsymbol{U}_{0}(mathbf{1}-cos boldsymbol{d} boldsymbol{x}) )
where ( U_{0} ) and ( d ) are constants. The time
period of small oscillations will be
в. ( 2 pi sqrt{frac{M}{U_{0} d^{2}}} )
( ^{mathbf{C}} cdot 2 pi sqrt{frac{U_{0} d^{2}}{M}} )
D. ( 2 pi sqrt{frac{U_{0}}{M d^{2}}} )
11
118ILLUSTRATION 33.9 To find the value of ‘g’ using simple
pendulum. T = 2.00 s;l = 1.00 m was measured. Estimate
maximum permissible error in ‘g’. Also find the value of ‘g’.
(use it = 10)
4726
11
119The number of independent constituent simple harmonic motions yielding a resultant displacement equation of the
periodic motion as ( boldsymbol{y}= )
( 8 sin ^{2}left(frac{t}{2}right) sin (10 t) ) is:
( A cdot 8 )
B. 6
( c cdot 4 )
( D .3 )
11
120A particle executes SHM given by the equation ( x=5 sin (3.14 t), x ) is measured in mms. The time period and the amplitude of the oscillations are
A. The amplitude is ( 5 mathrm{cms} ) and time period is 1 sec
B. The amplitude is 5 ( mathrm{mms} ) and time period is ( 1 mathrm{sec} )
c. The amplitude is ( 5 mathrm{mms} ) and time period is 3.142 seo
D. The amplitude is ( 5 mathrm{cms} ) and time period is 3.142 sec
11
121The variation of PE of a simple harmonic
oscillator is as shown. Then force
constant of the system is (PE ‘U’ is in
joules, displacement ( ^{prime} x^{prime} ) is in ( mathrm{mm} ) )
A. ( 100 mathrm{N} / mathrm{m} )
B. ( 150 mathrm{N} / mathrm{m} )
c. ( frac{200}{3} mathrm{N} / mathrm{m} )
D. ( 300 mathrm{N} / mathrm{m} )
11
122Two pendulums differ in lengths by
( 22 mathrm{cm} . ) They oscillate at the same place
so that one of them makes 30
oscillations and the other makes 36
oscillations during the same time. The lengths (in ( mathrm{cm} ) ) of the pendulums are
( mathbf{A} cdot 72 ) and 50
B. 60 and 38
c. 50 and 28
D. 80 and 58
11
123A spring is stretched by ( 0.20 m ) when a
mass of ( 0.50 mathrm{kg} ) is suspended. A mass of ( 0.25 mathrm{kg} ) is suspended, then its period
of oscillation will be ( left(g=10 m / s^{2}right) )
(approximately)
A ( .0 .628 s )
B. ( 0.251 s )
( mathbf{c} cdot 6.28 s )
D. 2.51s
11
124An oscillator consists of a block
attached to spring ( (mathrm{K}=1,1,400 mathrm{l}, mathrm{N} / mathrm{m}), mathrm{At} )
some time ( t, ) the position (measured from the system’s equilibrium location), velocity and acceleration of
the block are ( boldsymbol{x}=mathbf{0 . 1 0 0 m}, boldsymbol{v}= )
( -15.0 m / s, ) and ( a=-90 m / s^{2} . ) The
amplitude of the motion and the mass of the block are :
A. ( 0.2 m, 0.84 k g )
( g )
в. ( 0.3 m, 0.76 k g )
( mathrm{c} .0 .4 m, 0.54 mathrm{kg} )
D. ( 0.5 m, 0.44 k g )
11
125A glider is oscillating in SHM on an air track with an amplitude A. You slow it so that its amplitude becomes half.
Find the total mechanical energy in terms of previous value.
A ( cdot 1 / 2 )
в. ( 1 / 3 )
c. ( 1 / sqrt{5} )
D. ( 1 / 4 )
11
126A particle of mass ( m ) is oscillating with amplitude ( A ) and angular frequency ( omega ) its average energy in one time period is
?
A ( cdot frac{1}{2} m omega^{2} A^{2} )
B ( cdot frac{1}{4} m omega^{2} A^{2} )
( mathrm{c} cdot m omega^{2} A^{2} )
D. zero
11
127Which of the following quantities is
always negative in SHM?
This question has multiple correct options
( mathbf{A} cdot vec{F} cdot vec{a} )
в. ( vec{F} cdot vec{r} )
c. ( vec{v} . vec{r} )
D. vecू.न
11
128In SHM the net force towards mean
position is related to its displacement
(x) from mean position by the relation
( mathbf{A} cdot F propto x )
B . ( F propto frac{1}{x} )
c. ( F propto x^{2} )
D. ( F propto frac{1}{x^{2}} )
11
129A string of length ( 0.5 m ) carries a bob
with a period ( 2 pi s . ) Calculate the angle of
inclination of string with vertical and
tension in the string.
11
130The equation of a simple harmonic motion is ( boldsymbol{x}=mathbf{0 . 3 4} cos (mathbf{3 0 0 0 t}+mathbf{0 . 7 4}) )
where ( x ) and ( t ) are in ( mathrm{mm} ) and ( mathrm{sec} )
respectively. The frequency of the motion is :
A. 3000
B. 3000/2pi
c. ( 0.74 / 2 pi )
D. 3000/ ( pi )
11
131The displacement of a particle is
represented by the equation ( y=sin ^{3} omega t )
the motion is
A. Non-periodic
B. Simple harmonic with period ( pi / omega )
c. simple harmonic with period ( 2 pi / omega )
D. Periodic but not simple harmonic
11
132Vertical displacement of a plank with a body of mass ‘m’ on it is varying according to law ( y=sin omega t+sqrt{3} cos omega t )
The minimum value of ( omega ) for which the
mass just breaks off the plank and the
moment it occurs first after ( t=0 ) are
given by: ( y is positive vertically upwards)
A ( cdot sqrt{frac{g}{2}}, frac{sqrt{2}}{6} frac{pi}{sqrt{g}} )
В ( cdot frac{g}{sqrt{2}}, frac{2}{3} sqrt{frac{pi}{g}} )
c. ( sqrt{frac{g}{2}}, frac{pi}{3} sqrt{frac{2}{g}} )
D ( cdot sqrt{2 g}, sqrt{frac{2 pi}{3 g}} )
11
133The period of a particle in SHM is 8
seconds. At ( t=0 ) it is at the mean
position. The ratio of the distance traveled by it in the 1 st and the 2nd seconds is
A ( cdot frac{1}{2} )
B. ( frac{1}{sqrt{2}} )
( c cdot sqrt{2} )
D. ( sqrt{2}+1 )
11
134In simple harmonic motion, loss of kinetic energy is proportional to
( mathbf{A} cdot e^{x}^{x} )
B ( cdot x^{3} )
( c cdot log x )
D. ( x^{2} )
11
135( frac{frac{2}{2}}{frac{1}{2}} )11
136Mur man indower11
137The amplitude and time period of simple harmonic oscillator are ( a ) and ( T )
respectively. The time taken by it in
displacing from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=boldsymbol{a} / mathbf{2} ) will
be
A . ( T )
в. ( frac{T}{2} )
c. ( frac{T}{4} )
D. ( frac{T}{12} )
11
138Which of the following quantities connected with SHM do not vary
periodically?
A. Total energy
B. Velocity
c. Displacement
D. Acceleration
11
139For a mass on a spring, which is
maximized when the displacement of the mass from its equilibrium position is zero?
A. Frequency
B. Amplitude
c. Period
D. wavelength
E. Kinetic Energy
11
140A particle is performing S.H.M. with
acceleration ( a=8 pi^{2}-4 pi^{2} x ) where ( x ) is
coordinate of the particle w.r.t. the origin. The parameters are in S.I. units. The particle is at ( x=-2 a t t=0 ) then
find the coordinate of the particle ( boldsymbol{w} . boldsymbol{r} . boldsymbol{t} )
origin at any time ( t )
11
141The displacement-time graph of a
particle executing SHM is shown in the
figure. Then
This question has multiple correct options
A. the velocity is maximum at ( t=T / 2 )
B. the acceleration is maximum at ( t=T )
C. the force is zero at ( t=3 T / 4 )
D. the potential energy equals the oscillation at t=T/2
11
142Figures show a sinusoidal wave at a
given instant
Which points are in phase?
4.4 .8
B. В,
( c cdot B, D )
D. c.
11
143A particle is executing SHM of period 4s.Then the time taken by it to move from thr extreme position to ( frac{sqrt{3}}{2} ) of the amplitude is:
A ( cdot frac{1}{3} s )
в. ( frac{2}{3} ) s
c. ( frac{3}{4} )
D. ( frac{4}{3} ) s
11
144Frequency of variation of kinetic energy of a simple harmonic motion of
frequency n is
A . ( 2 n )
в. ( n )
( c cdot frac{n}{2} )
D. 3 n
11
145The frequency of a particle executing SHM is 10 Hz. The particle is suspended from a vertical spring. At the highest point of its oscillation, the spring is unstretched. Maximum speed of the
particle is ( (boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s} mathbf{2}) )
( ^{text {A }} cdot frac{1}{2 pi} m s )
в. ( frac{7}{2 pi} m s )
c. ( frac{5}{2 pi} m s )
D. ( frac{1}{3 pi} m s )
11
146In an SHM, the total energy of a particle
is
A . a constant
B. increases with time
c. decreases with time
D. oscillates with time
11
147A certain weight is attached to a spring It is pulled down and then released. It oscillates up and down. Its K.E. will be.
A. maximum at the middle of the movement
B. maximum at the bottom
c. maximum just before it is released
D. constant
11
148Time period of oscillation for given combination will be
A ( cdot 2 pi sqrt{frac{mleft(K_{1}+K_{2}right)}{K_{1} K_{2}}} )
в. ( 2 pi sqrt{frac{m}{K_{1}+K_{2}}} )
c. ( 2 pi sqrt{frac{m K_{1} K_{2}}{K_{1}+K_{2}}} )
D. ( 2 pi sqrt{frac{m K_{1}}{K_{2}}} )
11
149Identify which of the following system exhibit simple harmonic motion?
I. A simple pendulum with small deflection.
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
A. I only
B. II only
c. III only
D. I and II only
E . I, II, and III
11
150For periodic motion of small amplitude
( A, ) the time period ( T ) of this particle is
proportional to
( mathbf{A} cdot A sqrt{frac{m}{alpha}} )
B. ( frac{1}{A} sqrt{frac{m}{alpha}} )
c. ( A sqrt{frac{alpha}{m}} )
D. ( A sqrt{frac{2 alpha}{m}} )
11
151What type of curve do we get, if ( x^{2} ) and
( v^{2} ) are plotted for a particle executing ( mathrm{SHM}, mathrm{x} ) and ( mathrm{v} ) are the position and velocity of the particle:
A . Circle
B. Straight line
c. Ellipse
D. Rectangle
11
152For a particle executing SHM, which kinetic parameter will be equal to zero At equilibrium position,
A. velocity
B. acceleration
c. kinetic energy
D. none of the above
11
153The oscillations represented by curve 1
in the graph are expressed by equation
( x= ) Asinwt. The equation for the
oscillations represented by curve 2 is expressed as:
A. ( x=2 A sin (omega t-pi / 2) )
B. ( x=2 A sin (omega t+pi / 2) )
c. ( x=-2 operatorname{Asin}(omega t-pi / 2) )
D. ( x=operatorname{Asin}(omega t-pi / 2) )
11
154For a particle executing SHM. The KE ‘K’ is given by ( K=K_{0} cos ^{2} w t . ) The
maximum value of PE is
A. ( K_{0} )
B. zero
c. ( frac{K_{0}}{2} )
D. ( frac{K_{0}}{4} )
11
155A particle executing simple harmonic motion with an amplitude A. The distance travelled by the particle in one time period is
A. zero
B. A
c. 2 A
D. 4A
11
156An equilateral triangle has been constructed with an uniform wire whose
resistance per unit length is 4 ohm
( c m^{-1} . ) If the length of each side of the
triangle is ( 10 c, ) the resistance across any side will be
A. 80 ohm
B. 40 ohm
c. ( frac{80}{3} ) onm
D. ( frac{40}{3} ) ohm
11
157Force acting on a block is ( boldsymbol{F}=(-4 x+ )
8). Here ( F ) is in Newton and ( x ) the position of block on ( x ) -axis in meters
A. motion of the block is periodic but not simple harmonic
B. motion of the block is not periodic
c. motion of the block is simple harmonic about origin, ( x=0 )
D. motion of the block is simple harmonic about ( x=2 m ).
11
158Column 1
a) A linear S.H.M
e) ( frac{d^{2} Theta}{d t^{2}}=frac{c}{Theta} )
b) Angular S.H.M
f) ( frac{d^{2} x}{d t^{2}}+ )
( frac{boldsymbol{R}}{boldsymbol{m}} frac{boldsymbol{d} boldsymbol{x}}{boldsymbol{M} boldsymbol{t}}+boldsymbol{x} boldsymbol{w}^{2}=frac{boldsymbol{F}}{boldsymbol{m}} cos boldsymbol{theta} )
c) Damped harmonic
motion
g) ( frac{d^{2} x}{d t^{2}}- )
( frac{k}{m} x=0 )
d) forced oscillation
h) ( m frac{d^{2} x}{d t^{2}}+ )
( R frac{d n}{d t}+m x omega^{2}=0 )
A. a-e, ( b-h, c-g, d-f )
B. ( a-f, b-g, c-e, d-h )
( c cdot a-g, b-e, c-h, d-f )
D. a-g, b-h, c-e, d-f
11
159If the displacement of simple pendulum at any time is ( 0.02 m ) and acceleration
is ( 2 m / s^{2}, ) then in this time angular
velocity will be:
( mathbf{A} cdot 100 mathrm{rad} / mathrm{s} )
D. ( 0.1 mathrm{rad} / mathrm{s} )
11
160The equation of a simple harmonic motion is given by ( boldsymbol{x}=mathbf{6} sin mathbf{1 0 t}+ )
( 8 cos 10 t, ) where ( x ) is in ( mathrm{cm}, ) and ( t ) is in
seconds. Find the resultant amplitude
A . 20
B . 10
c. 30
D. 50
11
161The potential energy function for a
particle executing linear simple
harmonic motion is given by ( U(x)= )
( frac{1}{2} k x^{2}, ) where ( k ) is the force constant. For
( k=0.5 N m^{-1}, ) the ( operatorname{graph} ) of ( U(x) )
versus ( x ) is shown in figure. Show that a
particle of total energy ( 1 J ) moving
under this potential’ turns back’ when
it reaches ( boldsymbol{x}=pm mathbf{2} boldsymbol{m} )
11
162A sings with a frequency ( (n) ) and ( B ) sings with a frequency ( 1 / 8 ) that of ( A ). If
the energy remains the same
and the amplitude of ( A ) is ( a ), then
amplitude of ( boldsymbol{B} ) will be
A . ( 2 a )
B. ( 8 a )
c. ( 4 a )
D.
11
163The force on a particle of mass ( 10 g ) is ( (10 hat{i}+5 hat{j}) N . ) If it starts from rest, what
would be its position at time ( t=5 s ? )
A . ( (12500 hat{i}+6250 hat{j}) m )
B. ( (6250 hat{imath}+12500 hat{j}) m )
c. ( (12500 hat{i}+12500 hat{j}) m )
D. ( (6250 hat{i}+6250 hat{j}) m )
11
164The differential equation representing the SHM of a particuleis ( frac{mathbf{9 d}^{2} boldsymbol{y}}{boldsymbol{d t}^{2}}+mathbf{4} boldsymbol{y}=mathbf{0} )
The time period of the particle is given by
A ( cdot frac{pi}{3} sec )
в. ( pi ) sec
( ^{mathrm{c}} cdot frac{2}{pi} 3 s e c )
D. ( 3 pi s e c )
11
165The time taken by the particle in SHM for maximum displacement is ?
A. ( T / 8 )
B. T/6
( c cdot pi / 2 )
D. T/4
11
166The diagram in Fig. shows the
displacement- time graph of a vibrating
body. Name the kind of vibrations.
11
167Assertion (A): The displacement time graph for a particle in SHM begins from mean position. Reason
(R): The displacement of a particle in SHM is given by ( y=A sin omega t )
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is not the correct explanation of
C. A is true and R is false
D. A is false and R is true
11
168The displacement of a particle is
represented by the equation ( y= )
( sin ^{3}(omega t) . ) The motion is
A. non-periodic
B. periodic but not simple harmonic
c. simple harmonic with period ( frac{2 pi}{omega} )
D. simple harmonic with period ( frac{pi}{omega} )
11
169The average acceleration in one time period in a simple harmonic motion is
A ( cdot A omega^{2} )
B. ( A omega^{2} / 2 )
C. ( A omega^{2} / sqrt{2} )
D. zero
11
170Figure gives the ( x ) -t plot of particle executing one-dimensional simple harmonic motion.Give the signs of
position, velocity and acceleration variables of the particle at ( t=0.3 s, 1.2 s )
-1.2 s.
11
171Kinetic energy of the bob of a simple pendulum is maximum at the extreme left position. State whether true or false.
A. True
B. False
11
172What is the relation between restoring force ( (boldsymbol{F}) ) and displacement ( (boldsymbol{x}) ) of ( mathbf{a} ) particle to perform SHM.
A ( . F propto x^{2} )
B. ( F propto x^{-2} )
c. ( F propto x^{1 / 2} )
D. ( F propto x )
11
173A mass of ( 5 mathrm{kg} ) is suspended on a spring of stiffness ( 4000 mathrm{N} / mathrm{m} ). The system is fitted with a damper with a damping ratio of 0.2. The mass is pulled down 50 ( mathrm{mm} ) and released. Calculate the
displacement after 0.3 sec:
( mathbf{A} cdot 4.07 mathrm{mm} )
в. ( 4.7 mathrm{mm} )
( c .7 .4 mathrm{mm} )
D. 7.04 mm
11
174A simple pendulum is suspended from
the ceiling of a car accelerating
uniformly on a horizontal road. If the
acceleration is ( a_{0} ) and the length of the
pendulum is ( l ), find the time period of
position
( mathbf{A} )
B.
( ^{mathrm{C}} 2 pi frac{sqrt{l}}{left(a_{0}^{2}+g^{2}right)^{1 / 4}} )
D. ( pi frac{sqrt{l}}{left(a_{0}^{2}+g^{2}right)^{1 / 4}} )
11
175If a particle is executing ( S H M ) on a
straight line. ( A ) and ( B ) are two points at which its velocity is zero. It passes
through a certain point ( boldsymbol{P}(boldsymbol{A} boldsymbol{P}<boldsymbol{P B}) )
at successive intervals of 0.5 sec and
1.5 sec with a speed of ( 3 mathrm{m} / mathrm{s} ). The maximum speed of the particle is
A. ( 3 m / s )
B. ( 3 sqrt{2} mathrm{m} / mathrm{s} )
( mathbf{c} cdot 3 sqrt{3} m / s )
D. ( 6 m / s )
11
176The propagation of a sound wave in a gas is given by the equation ( frac{boldsymbol{d}^{2} boldsymbol{y}}{boldsymbol{d} boldsymbol{t}^{2}}=frac{boldsymbol{k}}{boldsymbol{l}} cdot frac{boldsymbol{d}^{2} boldsymbol{y}}{boldsymbol{d} boldsymbol{x}^{2}} )
Then the velocity of sound is given by
A ( cdot frac{k}{l} )
в. ( frac{l}{k} )
c. ( sqrt{left(frac{k}{l}right)} )
D. ( sqrt{left(frac{l}{k}right)} )
11
177A particle executes SHM with a period
of ( T ) seconds. ( t ) seconds after it has
crossed the equilibrium position it is at
a point ( P . ) After how much time it will be
again at ( P ? )
A ( cdot frac{T}{2}-t )
в. ( frac{T}{4}-t )
c. ( frac{T}{2}-2 t )
D. ( frac{T}{4}-2 t )
11
178Which of the following equations does not represent a simple harmonic motion
A. ( y-alpha omega t )
B. ( y=alpha omega t )
c. ( y=alpha omega t+b c o s omega t )
D. ( y=alpha ) tanct
11
179The amplitude of oscillation of a particle is 0.05 m.lf its period is 1.57 s. Then the velocity at the mean position
is
( A cdot 0.1 mathrm{m} / mathrm{s} )
B. ( 0.2 mathrm{m} / mathrm{s} )
( c cdot 0.3 mathrm{m} / mathrm{s} )
D. ( 0.5 mathrm{m} / mathrm{s} )
11
180An object performing S.H.M. with mass of ( 0.5 k g, ) force constant ( 10 N / m ) and amplitude ( 3 c m . ) What is the speed at ( x=2 ? )11
181The frequency of oscillation in an
oscillation is
A ( cdot frac{pi}{omega} )
в. ( frac{2 pi}{omega} )
c. ( frac{omega}{2 pi} )
D. ( frac{omega}{pi} )
11
182The motion of a particle executing SHM is given by ( boldsymbol{x}=mathbf{0 . 0 1} sin 100 pi(boldsymbol{t}+mathbf{0 . 0 5}) )
where ( x ) is in metre and ( t ) in second. The
time period of motion(in second) is:
A . 0.01
B. 0.02
c. ( 0 . )
D. 0.2
11
183Which of the following is an example of oscillatory motion?
A. Heart beat of a persion
B. Motion of earth around the sun
c. Motion of Hally’s comet around the sun
D. oscillations of a simple pendulam
11
184What are Damped vibrations?11
185The maximum displacement of a particle executing SHM from its mean position is ( 2 mathrm{cm} ) and its time period is 1
s. The equation of its displacement will be
A . ( x=2 sin 4 pi t )
B. ( x=2 sin 2 pi t )
c. ( x=sin 2 pi t )
D. ( x=4 sin 2 pi t )
11
186A particle executing SHM according to
the equation ( boldsymbol{x}=mathbf{5} cos left[mathbf{2} boldsymbol{pi} boldsymbol{t}+frac{pi}{4}right] ) in ( mathbf{S} )
units. The displacement and acceleration of the particle at ( t=1.5 ) s is:
A ( .-3.0 m, 100 m s^{-2} )
B . ( +2.54 m, 200 m s^{-2} )
c. ( -3.54 m, 140 m s^{-2} )
D. ( -3.55 m, 120 m s^{-2} )
11
187( sum_{k} )11
188A particle executes a simple harmonic motion of time period ( T . ) Find the time taken by the particle to go directly from its mean position to half the amplitude.
A ( cdot frac{T}{2} )
в. ( frac{T}{4} )
c. ( frac{T}{8} )
D. ( frac{T}{12} )
11
189Out of the following functions representing motion of particle which
represents SHM?
( x=sin ^{3} omega t )
2. ( x=1+omega t+omega^{2} t^{2} )
3. ( boldsymbol{x}=cos omega boldsymbol{t}+cos boldsymbol{3} boldsymbol{omega} boldsymbol{t}+boldsymbol{c} boldsymbol{o} boldsymbol{s} boldsymbol{5} boldsymbol{t} )
4. ( x=sin omega t+cos omega t )
A. Only 1
B. Only 1 and 3
c. only 1 and 4
D. only 4
11
190A rod of moment of inertia I and length
is suspended from a fixed end and
given small oscillations about the point of suspension, the restoring torque is
found to be ( -(boldsymbol{m} boldsymbol{g} boldsymbol{L} / mathbf{2}) boldsymbol{s} boldsymbol{i} boldsymbol{n} boldsymbol{theta} . ) What will
be the angular equation of motion of the
SHM
A ( cdot frac{d^{2} theta}{d t^{2}}+(m g L / I) theta=0 )
B ( cdot frac{d^{2} theta}{d t^{2}}+(m g L / 2 I) theta=0 )
( ^{mathbf{c}} cdot frac{d^{2} theta}{d t^{2}}+(2 m g L / I) theta=0 )
D. ( frac{d^{2} theta}{d t^{2}}+(m g L / 4 I) theta=0 )
11
191Mass ( m_{1} ) hits and sticks with ( m_{2} ) while
sliding horizontally with velocity ( v ) along the common line of centres of the three
[
text { equal masses }left(boldsymbol{m}_{1}=boldsymbol{m}_{2}=boldsymbol{m}_{3}=boldsymbol{m}right)
]
Initially masses ( m_{2} ) and ( m_{3} ) are stationary and the spring is unstretched. Minimum kinetic energy of
( m_{2} ) is ( y m v^{2} / 36 . ) Find ( y )
11
192Assertion
A particle is moving along x-axis. The resultant force ( boldsymbol{F} ) acting on it at
position ( x ) is given by ( F=-a x-b )
Where ( a ) and ( b ) are both positive constants. The motion of this particle is
not SHM
Reason
In SHM, restoring force must be proportional to the displacement from mean position.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
193If ( x ) denotes displacement in time ( t ) and
( boldsymbol{x}=boldsymbol{a} cos omega boldsymbol{t}, ) then for ( boldsymbol{omega}=mathbf{1}, ) the
acceleration will be
( mathbf{A} cdot a cos t )
B. – a cost
( mathbf{c} cdot a sin t )
D. – ( a sin t )
11
194Two particles A and B perform SHM along the same straight line with the same amplitude ‘a’, same frequency ‘f and same equilibrium position ‘0’. The greatest distance between them is found to be ( 3 a / 2 ). at some instant of
time they have the same displacement from mean position. What is this displacement?
A ( cdot frac{a}{sqrt{2}} )
B. ( a sqrt{7} / 4 )
c. ( sqrt{7} a / 4 )
D. 3a/4
11
195A particle undergoes SHM. When its displacement is ( 8 mathrm{cm}, ) it has speed 3 ( mathrm{m} / mathrm{s} ) and a speed ( 4 mathrm{m} / mathrm{s} ) at displacement of ( 6 mathrm{cm} . ) Find time period of oscillation.
A . ( 4 pi )
в. ( 6 pi )
c. ( 7 pi )
D. ( 8 pi )
11
196Two blocks ( A ) and ( B ), each of mass ( m ), are
connected by a massless spring of natural length L and spring constant k. The blocks are initially resting on a smooth horizontal floor with the spring
at its natural length as shown in Fig. A
third identical block ( C ), also of mass ( m )
moves on the floor with a speed ( mathbf{v} ) along the line joining ( A ) and ( B ) and collides with ( A, ) then
This question has multiple correct options
A. The KE of the AB system at maximum compression of the spring is zero.
B. The KE of the AB system at maximum compression of the spring is ( (1 / 4) m v^{2} )
c. The maximum compression of the spring is ( v sqrt{frac{m}{k}} )
D. The maximum compression of the spring is ( v sqrt{frac{m}{2 k}} )
11
197A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy (K.E.) and total energy (T.E.) are measured as a function
of time t. Which of the following statements is true. Assume that the
particle started at ( t=0 ) at its mean position
A. P.E. is maximum when ( t=0 )
B. T.E. is zero when ( t=0 )
c. K.E. is maximum when ( t=0 )
D. K.E. is minimum when t =
11
198The time period of a particle executing SHM is 2 s. After what time interval from ( t=0, ) will its displacement be half the amplitude:
( A cdot(1 / 4) sec s )
B. (1/3) secs
c. (1/2) secs
D. 1 sec
11
199Two particles executing SHM of same frequency, meet at ( x=+A / 2, ) while
moving in opposite directions. Phase difference between the particles is
11
200A long spring when stretched by ( x c m )
has a potential energy ( v . ) On increasing the stretching to ( n x c m, ) the potential energy stored in the spring will be
A ( . n v )
B . ( n^{2} v )
( c cdot n v^{3} )
D. ( n v^{-2} )
11
201The force of a required to row a boat at velocity is proportional to square of its speed of ( mathbf{v} mathrm{km} / mathrm{h} ) requires ( 4 mathrm{KW}, ) how many does a seepd of ( 2 mathrm{V} mathrm{km} / mathrm{h} ) required
( A cdot 8 mathrm{kW} )
B. 16 kw
c. з२кw
D. 76kw
11
202A particle is an oscillating simple
harmonically with angular frequency ( omega )
and amplitude ( A ). It is at a point ( (A) ) at ( a )
certain instant (shown in the figure). At
this instant, it is moving towards mean
position (B). It takes time ( t ) to reach mean position (B). If the time period of oscillation is ( T, ) the average speed
between ( A ) and ( B ) is :
A. ( frac{A sin omega t}{t} )
B. ( frac{A cos omega t}{t} )
c. ( frac{A sin omega t}{T} )
D. ( A cos omega t )
11
203In reality, a spring won’t oscillate for
ever. will ( quad ) the amplitude of oscillation until eventually the system is at rest.
A. Frictional force, increase
B. Viscous force, decrease
c. Frictional force, decrease
D. Viscous force, increase
11
204A plank with a small block on top of it is undergoing vertical SHM. Its period is 2 sec.The minimum amplitude at which the block will separate from plank is :
A ( cdot frac{10}{pi^{2}} )
в. ( frac{pi^{2}}{10} )
c. ( frac{20}{pi^{2}} )
D. ( frac{pi}{10} )
11
205A partical having mass 10 g oscillates according to the equation ( boldsymbol{x}= ) ( (2.0 c m) sin left[left(100 s^{-1}right) t+frac{6}{pi}right] . ) Find
(a) the amplitude, the time period and
the force constant
(b) the position, the velocity and the
acceleration at ( t=0 )
11
206The displacement equations of two simple harmonic oscillators are given by ( boldsymbol{x}_{1}=boldsymbol{A}_{1} cos boldsymbol{omega} boldsymbol{t} ; boldsymbol{x}_{2}=boldsymbol{A}_{2} sin left(boldsymbol{omega} boldsymbol{t}+frac{pi}{6}right) )
The phase difference between them is:
( A cdot 30 )
B. 60
( c cdot 90 )
D. ( 120^{circ} )
11
207The relation between ( T ) and ( g ) by
( mathbf{A} cdot T propto g )
в. ( T propto g^{2} )
c ( cdot T^{2} propto g^{-1} )
D ( T propto frac{1}{g} )
11
208A particle is executing simple harmonic simple motion of amplitude ( 5 mathrm{cm} ) and period 6 s. How long will it take to move from one end of its path on one side of mean position to a position ( 2.5 mathrm{cm} ) on the same side of the mean position?
A . ( 1 mathrm{s} )
B. 1.5 s
( c cdot 3 s )
D. 3.5
11
209For the damped oscillator shown in Fig
the mass of the block is ( 200 g, k= )
( 80 N m^{-1} ) and the damping constant ( b )
is ( 40 g s^{-1} ) Calculate.
(a) The period of oscillation,
(b) Time period for its amplitude of
vibrations to drop to half of its initial
value
(c) The time for the mechanical energy
to drop to half initial value.
11
210The oscillations of a pendulum slow
down due to:
A. the force exerted by air and the force exerted by friction at the support
B. the force exerted by air only
C. the forces exerted by friction at the support
D. they never slow down
11
211A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant ‘b’, the correct equivalence would be :
A. ( L leftrightarrow m, C leftrightarrow k, R leftrightarrow b )
в. ( L leftrightarrow frac{1}{b}, C leftrightarrow frac{1}{m}, R leftrightarrow frac{1}{k} )
c. ( L leftrightarrow k, C leftrightarrow b, R leftrightarrow m )
D ( cdot L leftrightarrow m, C leftrightarrow frac{1}{k}, R leftrightarrow b )
11
212On the average a human heart is found to beat 75 times in a minute. Calculate
its beat frequency of heart and period.
11
213A particle executes ( boldsymbol{S H} boldsymbol{M} ) on a line
( 8 c m ) long. Its ( K . E ) and ( P . E ) will be equal
when its distance from the mean
position is:
A. ( 4 mathrm{cm} )
B. 2 cm
( mathrm{c} cdot 2 sqrt{2} mathrm{cm} )
D. ( sqrt{2} ) cm
11
214toppr
frictionless surface. The block is
stretched by ( 0.2 m ) and released from
rest at ( t=0 . ) It then executes simple
harmonic motion with angular frequency ( omega=frac{pi}{3} r a d / s )
Simultaneously at ( t=0, ) a small
pebble is projected with speed ( boldsymbol{v} ) from
point ( P ) at an angle of ( 45^{circ} ) as shown in
the figure. Point ( P ) is a a horizontal
distance of ( 10 mathrm{m} ) from ( mathrm{O} ). If the pebble
hits the block at ( t=1 ) sec, the value of ( v )
is ( left(operatorname{take} g=10 m / s^{2}right): )
( mathbf{A} cdot sqrt{50} m / s )
B. ( sqrt{51} mathrm{m} / mathrm{s} )
( mathbf{c} cdot sqrt{52} m / s )
D. ( sqrt{53} mathrm{m} / mathrm{s} )
11
215Two pulses in a stretched string whose centers are initially ( 8 mathrm{cm} ) apart are moving towards each other as shown in figure. The speed of each pulse is 2 ( mathrm{cm} / mathrm{s} . ) After 2 seconds, the total energy
of the pulses will be :
A . zero
B. purely kinetic
c. purely potential
D. partly kinetic and partly potential
11
216A particle of mass in oscillates with
simple harmonic motion between two
points ( x_{1} ) and ( x_{2}, ) the equilibrium
position being a Its potential energy is plotted on the graph. Which of the
following curve represents the phenomenon?
A
(a)
B.
c.
D.
11
217The phase difference between the velocity and displacement of a particle executing SHM is
A ( cdot pi / 2 ) radian
( c cdot 2 pi ) radian
D. zero
11
218A train is moving at ( 30 m s^{-1} ) in still air. The frequency of the locomotive whistle
is ( 500 mathrm{Hz} ) and the speed of sound is 345
( m s^{-1} . ) The apparent wavelengths of sound in-front of and behind the
locomotive are respectively.
A. ( 0.65 mathrm{m}, 0.73 mathrm{m} )
B. ( 0.63 mathrm{m}, 0.75 mathrm{m} )
c. ( 0.60 mathrm{m}, 0.85 mathrm{m} )
D. ( 0.60 mathrm{m}, 0.75 mathrm{m} )
11
219Figure shows three systems in which a
block of mass m can execute S.H.M.
What is ratio of frequency of
oscillation?
( A cdot 2: 1: 4 )
B. 1: 2: 4
c. 4: 2: 1
D. 3: 2:
11
220Define phase of ( boldsymbol{S} . boldsymbol{H} . boldsymbol{M} ) ?11
221The figure shows an assembly
consisting of a number of pendulums of
varying lengths. The driver pendulum is pulled aside and released so that it
oscillates in a plane perpendicular to
that of the diagram.
It will be observed that :
A. all pendulums oscillate with the frequency of the driver pendulum and have the same amplitude.
B. pendulums oscillate with different frequencies but equal amplitude, the shortest pendulum oscillating with the highest frequency,
c. all pendulums oscillate with the frequency of the driver pendulum; the pendulum with length equal to that of the driver has the greatest amplitude
D. pendulums oscillate with different frequencies and rent amplitudes
11
222During the oscillations of a simple pendulum, the string takes the same
path as that of the bob, then:
A. motion of the bob and string are in SHM
B. motion of the bob is SHM and that of the string is s angular SHM
c. motion of the bob and string are angular SHM
D. None of the above
11
223Displacement vs time curve for a
particle SHM is as shown in the figure:
Which of the following statements is
correct?
A. Phase of the oscillator is same at ( t=0 ) s and ( t=2 ) s
B. Phase of the oscillator is same at ( t=2 ) s and ( t=5 ) s
c. Phase of the oscillator is same at ( t=1 ) s and ( t=7 ) s
D. Phase of the oscillator is same at ( t=1 ) s and ( t=5 ) s.
11
224A particle (1) of mass m initially at A is at rest. The radius of circular path is 1
m. The particle (1), collides at bottom
with an other particle (2) of same mass
m. The distance travelled by the particle
(2) before coming at rest is
( 4.1 .5 mathrm{m} )
B. 2.5
( c .3 .5 mathrm{m} )
( D )
11
225You are riding in an automobile of mass 3000 kg. Assuming that you are examining the oscillation characteristics of its suspension system. The suspension sags ( 15 mathrm{cm} ) when the entire automobile is places on ¡t. Also the amplitude of oscillation decreases by 50% during one complete oscillation. Estimate the values of
(a) the spring constant ( k ) and
(b) the damping constant b for the
spring and shock absorber system of one wheel, assuming that each wheel supports ( 750 mathrm{kg} )
11
226Sitar maestro Ravi Shankar is playing sitar on its strings, and you, as a physicist (unfortunately without musical ears!), observed the following oddities.
I. The greater the length of a vibrating string, the smaller its frequency.
II. The greater the tension in the string, the greater is the frequency.
III. The heavier the mass of the string, the smaller the frequency.
IV. The thinner the wire, the higher its frequency. The maestro signalled the following combination as correct one.
A. II, III and IV
B. ।, / I and IV
c. ।, ॥ land III
D. I, II, III and IV
11
227If we wish to represent the equation for the position of the mass in terms of a differential equation, which one of
these would be the most suitable?
A ( cdot quad m frac{d^{2} x}{d t^{2}}+b frac{d x}{d t}+k x=0 )
в. ( quad_{m} frac{d^{2} x}{d t^{2}}-b frac{d x}{d t}+k x=0 )
c. ( _{m} frac{d^{2} x}{d t^{2}}+b frac{d x}{d t}-k x=0 )
D. ( _{m} frac{d^{2} x}{d t^{2}}-b frac{d x}{d t}-k x=0 )
11
228A particle performs SHM with a period ( boldsymbol{T} )
and amplitude ( a ). The mean velocity of
particle over the time interval during which it travels a distance ( a / 2 ) from the extreme position is:
( ^{A} cdot frac{6 a}{T} )
в. ( frac{2 a}{T} )
( c cdot frac{3 a}{T} )
D. None
11
229A block of mass ( m ) containing a net positive charges ( q ) is placed on a smooth horizontal table which
terminates in a ventricles wall as shown
in figure ( (29 . E 2) . ) The distance of the
block from the wall is ( d . ) A horizontal
electric field ( E ) towards right is
switched on. Assuming elastic collisions ( if any) find the time periods of the resulting oscillatory motion. Is it a simple harmonic motion?
11
230A particle is executing SHM along the ( x )
axis given by ( x=A ) sinomegat. What is the mangnitude of the average acceleration of the partical between ( t=0 ) and ( (T / 4) s ) where ( T ) is the time period of oscillation
11
231Assertion
All small oscillations are simple harmonic in nature.
Reason
Oscillations of spring block system are always simple harmonic whether amplitude is small or large.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
232Assertion : If the amplitude of a simple harmonic oscillator is doubled, its total
energy becomes double. Reason : The total energy is directly proportional to the amplitude of vibration of the harmonic oscillator.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
11
233A particle is executing ( S H M ) and its velocity ( v ) is related to its position ( (x) )
as ( y^{2}+a x^{2}=b, ) where a and b are
positive constants. The frequency of oscillation of particle is
( ^{A} cdot frac{1}{2 pi} sqrt{frac{b}{a}} )
B. ( frac{sqrt{a}}{2 pi} )
( c cdot frac{sqrt{b}}{2 pi} )
D. ( frac{1}{2 pi} sqrt{frac{a}{b}} )
11
234A transverse wave is passing through a medium. The maximum speed of the vibrating particle occurs when the displacement of the particle from the mean position is
A. zero
B. half of the amplitude
c. equal to the amplitude
D. none of the above
11
235A simple harmonic oscillator has an
amplitude a and time period T. The time required by it to a travel from ( x=a ) to ( x= ) a/2 is
A. ( T / 6 )
B. T / 4
( c cdot T / 3 )
D. T/2
11
236For a particle performing linear S.H.M. Its average speed over one oscillation is ( (a=a m p l i t u d e text { of } S . H . M, n= ) frequency of oscillation)
A . ( 2 a n )
B. 4an
c. ( 6 a n )
D. ( 8 a n )
11
237A person wearing a wrist watch that
keeps correct time at the equator goes to N-pole. His watch will
A. Keep correct time
B. gain time
c. loose time
D. cannot say
11
238The equation of the displacement of two particles making SHM are represented by
( boldsymbol{y}_{1}=a sin (omega t+phi) & boldsymbol{y}_{2}=a cos (boldsymbol{omega} boldsymbol{t}) )
The phase difference of the velocities of the two particles is :
( mathbf{A} cdot frac{pi}{2}+phi )
B. ( -phi )
c. ( phi )
D. ( phi-frac{pi}{2} )
11
239The disk has a weight of ( 100 mathrm{N} ) and rolls without slipping on the horizontal surface as it oscillates about its
equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the
equation which describes its oscillatory motion when it is released.
A ( cdot theta=-0.2 cos (16.16 t) )
B ( cdot theta=0.2 cos (16.16 t) )
c. ( theta=-0.4 cos (16.16 t) )
11
240The time period of a seconds’ pendulum
A. 1 second
B. 2 seconds
c. 3 seconds
D. 4 seconds
11
241A particle is in S.H.M of amplitude ( 2 mathrm{cm} )
At extreme position the force is ( 4 mathrm{N} ). At the point mid-way between mean and extreme position, the force is :
A. 1 N
B. 2N
c. 3 N
D. 4 N
11
242A particle is an linear simple harmonic motion between two extreme point ( mathbf{A} ) and B. ( 10 mathrm{cm} ) apart(See figure below) If the direction from ( A ) to ( B ) is taken as
positive direction, what are signs of displacement ( x, ) velocity ( V ) and acceleration a, when the particle is at
( mathbf{A} ? )
A ( . x=-v e, V=-v e, a=-v e )
в. ( x=+v e, V=0, a=-v e )
c. ( x=+v e, V=-v e, a=+v e )
D. ( x=-v e, V=0, a=+v e )
11
243Find time period of ( mathrm{SHM}=? )11
244The quantity ( frac{b}{2 sqrt{m k}} ) is called
A. critical coefficient
B. damping coefficient
C. friction coefficient
D. None of these
11
245Two particles are executing simple harmonic motion of the same
amplitude ( A ) and frequency ( omega ) along the x-axis. Their mean position is separated by distance ( boldsymbol{X}_{mathbf{0}}left(boldsymbol{X}_{mathbf{0}}>boldsymbol{A}right) . ) If the
maximum separation between them is
( left(X_{0}+Aright), ) the phase difference between
their motion is
( mathbf{A} cdot pi / 2 )
в. ( pi / 3 )
c. ( pi / 4 )
D. ( pi / 6 )
11
246A particle executes SHM with a time period of 4 s. At what instant of time, will the displacement of the particle be equal to the velocity of the particle
( A cdot 4 s )
B. 1 s
( c cdot 8 s )
D. Displacement and velocity cannot be equal at any instant
11
247toppr
time period is proportional to ( sqrt{frac{boldsymbol{m}}{boldsymbol{k}}}, ) as can be seen easily using dimensional analysis. However, the motion of a
particle can be periodic even when its
potential energy increases on both
sides of ( x=0 ) in a way different from
( k x^{2} ) and its total energy is such that the
particle does not escape to infinity.
Consider a particle of mass m moving
on the ( x ) -axis. Its potential energy is
( V(x)=alpha x^{4}(alpha>0) ) for ( |x| ) near the
origin and becomes a constant equal to
( V_{0} ) for ( |x| geq X_{0}(text { see figure }) )
The acceleration of this particle for
( |boldsymbol{x}|>boldsymbol{X}_{0} ) is?
A. Proportional to ( V_{0} )
B. Proportional to ( frac{V_{0}}{m X_{0}} )
C. Proportional to ( sqrt{frac{V_{0}}{m X_{0}}} )
D. Zero
11
248A simple harmonic oscillation has an amplitude ( A ) and time period ( T . ) The time required to travel from ( boldsymbol{x}=boldsymbol{A} ) to
( boldsymbol{x}=frac{boldsymbol{A}}{2} ) is :
A ( cdot frac{T}{6} )
в. ( frac{T}{4} )
c. ( frac{T}{3} )
D. ( frac{T}{12} )
11
249For what phase difference between two
SHMs will the amplitude of the
resultant SHM be zero
A . ( pi / 2 )
в. ( 2 pi )
( c . pi )
D. 0
11
250A particle executes SHM with
amplitude ( 0.5 mathrm{cm} ) and frequency ( 100 s^{-1} ) The maximum speed of the particle is ( (operatorname{in} m / s) )
( A )
B. 0.5
c. ( 5 pi times 10^{-5} )
D. ( 100 pi )
11
251The phenomenon in which the amplitude of oscillation of a pendulum decreases gradually is called
A. decay period of oscillation
B. damping
c. building up of oscillation
D. maintained oscillation
11
252The angular frequency of a spring block system is ( omega_{0} ) This system is suspended from the ceiling of anelevator moving
downwards with a constant speed ( v_{0} )
The block is at rest relative to the
elevator. Lift issuddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:
A ( cdot ) The amplitude of the block is ( frac{v_{0}}{omega_{0}} )
B. The initial phase of the block is ( pi )
C . The equation of motion for the block is ( frac{v_{0}}{omega_{0}} sin omega_{0} mathrm{t} )
D. The maximum speed of the block is ( v_{0} )
11
253Calculate the period of a wave, which is having the wavelenght ( 17 ~ m ) and wave velocity ( 340 m / s )11
254A particle performs SHM given by the
equation ( boldsymbol{x}= )Asinwt. Where is the
particle at ( t=3 T / 8 )
A. The particle is at a distance of ( A / sqrt{(} 2) ) moving away from the mean position to its extreme
B. The particle is at a distance of ( A / sqrt{(} 2) ) moving towards the mean position to its extreme
C. The particle is at a distance of ( A(1-1 / sqrt{(} 2)) ) moving away from the mean position to its extreme
D. None of these
11
255A solid sphere of mass ( 2 mathrm{kg} ) is rolling on a frictionless horizontal surface with
velocity ( 6 m / s . ) It collides on the free end of an ideal spring whose other end is fixed. The maximum compression produced in the spring will be (Force constant of the spring ( =mathbf{3 6} N / boldsymbol{m} )
A ( cdot sqrt{14 m} )
в. ( sqrt{2.8} m )
c. ( sqrt{1.4 m} )
D. ( sqrt{0.7} m )
11
256A particle oscillates simple harmonically with a period of 16 s. Two second after crossing the equilibrium position its velocity becomes ( 1 mathrm{m} / mathrm{s} ). The amplitude is
A ( cdot frac{pi}{4} mathrm{m} )
B. ( frac{8 sqrt{2}}{pi} mathrm{m} )
c. ( frac{8}{pi} mathrm{m} )
D. ( frac{4 sqrt{2}}{pi} mathrm{m} )
11
257The time period of periodic motion is
calculated using
A. Number of metres covered in 1 sec
B. Number of 90 degree turns covered in 1 sec
C. Number of oscillations per sec
D. Number of hairpin bends particle covers in 1 sec
11
258The equation of displacement of a particle executing SHM is ( boldsymbol{x}= ) ( 0.40 cos (2000 t+18) . ) The frequency of
the particle is
( mathbf{A} cdot 10^{3} mathrm{Hz} )
B. ( 20 mathrm{Hz} )
c. ( 2 times 10^{3} mathrm{Hz} )
D. ( frac{10^{3}}{pi} mathrm{Hz} )
11
259A solid ball of mass ( mathrm{m} ) is made to fall
form a height ( mathrm{H} ) on a pan suspended through a spring of spring constant ( mathrm{K} ) as shown in figure. if the ball does not rebound and the pan is mass less, then
amplitude of oscillation is
( A cdot frac{m g}{K} )
( ^{mathrm{B}} cdot frac{m g}{K}left(1+frac{2 H K}{m g}right)^{1 / 2} )
( ^{mathrm{c}} frac{m g}{K}+left(frac{2 H K}{m g}right)^{1 / 2} )
( ^{mathrm{D}} cdot frac{m g}{K}left[1+left(1+frac{2 H K}{m g}right)^{1 / 2}right] )
11
260A particle performs SHM with amplitude ( 25 mathrm{cm} ) and period 3s. The minimum time required for it to move between two mean positions is :
A . 0.6 s
в. 0.5 s
( c cdot 0.4 mathrm{s} )
D. 0.2 s
11
261A particle performs S.H.M of amplitude A along a straight line. When it is at a
distance ( frac{sqrt{3}}{2} A ) from mean position, its kinetic energy gets increased by an amount ( frac{1}{2} m omega^{2} A^{2} ) due to an impulsive force. Then its new amplitude becomes.
A. ( frac{sqrt{5}}{2} )
B. ( frac{sqrt{3}}{2} ) A
c. ( sqrt{2} mathrm{A} )
D. ( sqrt{5} mathrm{A} )
11
262A particle is in SHM. Then the graph of its acceleration as a function of
displacement is a
A . circle
B. hyperbola
c. straight line with negative slope
D. straight line with positive slope
11
263Three masses of ( 500 g, 300 g ) and ( 100 g )
are suspended at the end of a spring as shown and are in equilibrium. When the
( 500 g ) mass is removed suddenly, the
system oscillates with a period of 2
second. When the ( 300 g ) mass is also
removed, it will oscillate with a period
( mathbf{A} cdot 2 sec )
B. 4 sec
c. 8 sec
D. 1 sec
11
264The time period of a particle executing
( boldsymbol{S H} boldsymbol{M} ) is ( boldsymbol{8} boldsymbol{s} . ) At ( boldsymbol{t}=boldsymbol{0} ) it is at the mean
position. The ratio of distance covered
by the particle in ( 1^{s t} ) second to the ( 2^{n d} ) second is
A ( cdotleft(frac{1}{sqrt{2}-1}right) )
B. ( sqrt{2} )
c. ( (sqrt{2}+1) )
D. ( frac{1}{sqrt{2}} )
11
265The maximum velocity of a particle, executing simple harmonic motion with an amplitude ( 7 m m, ) is ( 4.4 m / s . ) The period of oscillation is
A. ( 100 s )
B. ( 0.01 s )
( c cdot 10 s )
D. ( 0.1 s )
11
266For a horizontal rod of moment of inertia
I if a constant force ( F ) acts on the rod at
an angle ( theta ) with the horizontal, the
torque equation for the rod will be (NOTE: The rod is lying on a floor horizontally)
A ( cdot I d^{2} theta / d t^{2}=2 F L theta )
B . ( I d^{2} theta / d t^{2}=F L theta )
( mathbf{c} cdot I d^{2} theta / d t^{2}=(F L / 2) )
D. None of the above
11
267Motion of an oscillating liquid in a
tube is
A. periodic but not simple harmonic
B. non-periodic
C. simple harmonic and time period is independent of the density of the liquid.
D. simple harmonic and time period is directly proportional to the density of the liquid
11
268A simple harmonic motion has an amplitude ( A ) and time period ( T . ) Find the time required by it to travel directly from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=boldsymbol{A} / mathbf{2} )11
269A mass of ( 30 mathrm{kg} ) is supported on a spring of stiffness ( 60000 mathrm{N} / mathrm{m} ). The system is damped and the damping ratio is ( 0.4 . ) The mass is raised ( 5 mathrm{mm} )
and then released. Calculate the
damped frequency in Hz.
A. 6.235
B. 6.352
c. 6.523
D. 6.325
11
270Two particle are oscillating along two close parallel straight lines side by side with the same frequency and amplitudes. They pass each other, moving in opposite directions when their displacement is half of the amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is:
A . 0
в. ( 2 pi / 3 )
( c )
D. ( pi / 6 )
11
271Which one of the following statements is true for the velocity v and the acceleration a of a particle executing simple harmonic motion?
A. When v is maximum, a is zero
B. When v vis zero, a is zero
c. When v is maximum, a is maximum
D. Value of a is zero, whatever may be the value of ( v )
11
272A particle is executing S.H.M. with amplitude A and Time period T. Time
taken by the particle to reach from
extreme position to ( frac{A}{2} )
( A cdot frac{T}{6} )
B・亞
( c cdot frac{T}{3} )
( D cdot frac{T}{4} )
11
273The potential energy of a particle with displacement ( x ) is ( U(x) . ) The motion is simple harmonic. If k is a positive
constant then
A ( cdot U=k x )
B. ( U=k )
c. ( U=-k x^{2} / 2 )
( mathbf{D} cdot U=k x^{2} )
11
274A particle has a rectilinear motion and
the figure gives its displacement as a function of time. Which of the following
statements is false with respect to the
motion?
A. Between O and A the velocity is positive and acceleration is negative
B. Between A and B the velocity and acceleration are positive
c. Between B and C the velocity is negative and acceleration is positive
D. Between C and D the acceleration is positive
11
275The displacement of a particle executing simple harmonic motion is
given by ( boldsymbol{y}=boldsymbol{A}_{0}+boldsymbol{A} sin omega boldsymbol{t}+boldsymbol{B} cos boldsymbol{omega} boldsymbol{t} )
Then the amplitude of its oscillation is given by :
( mathbf{A} cdot A_{0}+sqrt{A^{2}+B^{2}} )
B. ( sqrt{A^{2}+B^{2}} )
c. ( sqrt{A_{0}^{2}+(A+B)^{2}} )
D. ( A+B )
11
276A particle is executing SHM along a straight line. Its velocities at distances
( x_{1} ) and ( x_{2} ) from the mean position are ( V_{1} )
and ( V_{2} ) respectively. Its time period is:
A ( cdot 2 pi sqrt{frac{V_{1}^{2}-V_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}} )
B ( cdot 2 pi sqrt{frac{x^{2}+x_{2}^{2}}{sqrt{1}+V_{2}^{2}}} )
C ( cdot 2 pi sqrt{frac{x^{2}-x^{2}}{V_{2}^{2}-V_{1}^{2}}} )
D. ( 2 pi sqrt{frac{v^{2}+V_{2}^{2}}{x^{2}+x_{2}^{2}}} )
11
277When a body is undergoing undamped vibration, the physical quantity that remains constant is
A. amplitude
B. velocity
c. acceleration
D. phase
11
278The force on a particle of mass ( 10 g ) is ( (10 hat{i}+5 hat{j}) N . ) If it starts from rest, what
would be its position at time ( t=5 s ? )
A . ( (12500 hat{i}+6250 hat{j}) m )
B. ( (6250 hat{imath}+12500 hat{j}) m )
c. ( (12500 hat{i}+12500 hat{j}) m )
D. ( (6250 hat{i}+6250 hat{j}) m )
11
279In simple harmonic motion, the acceleration is inversely proportional to the displacement of the body from its mean position.
A. True
B. False
c. Nither
D. Either
11
280A particle of mass ( 1 mathrm{kg} ) is moving in a
S.H.M with an amplitude of ( 0.02 mathrm{m} ) and a frequency of ( 60 mathrm{Hz} ). The maximum force acting on the particle is :
A ( .2 .88 times 10^{3} mathrm{N} )
B . ( 1.44 times 10^{3} ) N
c. ( 5.67 times 10^{3} mathrm{N} )
D. ( 0.75 times 10^{3} mathrm{N} )
11
281A mass of ( 50 mathrm{kg} ) is suspended from a spring of stiffness ( 10 mathrm{kN} / mathrm{m} ). It is set oscillating and it is observed that
two successive oscillations have
amplitudes of ( 10 mathrm{mm} ) and ( 1 mathrm{mm} ) Determine the damping ratio.
A. 0.315
B. 0.328
c. 0.344
D. 0.353
11
282n figure, ( boldsymbol{k}=mathbf{1 0 0} boldsymbol{N} / boldsymbol{m}, boldsymbol{M}= )
1 kgand ( F=10 N . ) A sharp blow by
some external agent imparts a speed of ( 2 m / s ) to the block towards left. Find the
sum of the potential energy of the spring and the kinetic energy of the block at this instant.
A . ( 0.25 J )
в. 1.5
( c cdot 2 J )
D. 2.5 5
11
283A body of mass ( 36 g m ), moves with
S.H. ( M ) of amplitude ( A=13 mathrm{cm} ) and
period ( boldsymbol{T}=mathbf{1 2} ) sec. At a time ( boldsymbol{t}=mathbf{0}, ) the
displacement is ( boldsymbol{x}=+mathbf{1 3} ) cm. The
shortest time of passage from ( boldsymbol{x}= )
( +6.5 mathrm{cm} ) to ( x=-6.5 ) is ?
( mathbf{A} cdot 4 sec )
B. 2 sec
( mathrm{c} cdot 6 mathrm{sec} )
D. 3 sec
11
284Two equal charges ( q ) are kept fixed at ( a )
and ( +a ) along the ( x ) -axis. A particle of mass ( m ) and charge ( frac{q}{2} ) is brought to the origin and given a small displacement along the ( x ) -axis, then:
A. the particle executes oscillatory motion
B. the particle remains stationary
c. the particle executes, SHM along x-axis
D. the particle executes SHM along y-axis
11
285simple harmonic motion, then correct
graph for acceleration ( ^{prime} a^{prime} ) and
corresponding linear velocity’ ( v^{prime} ) is :
( A )
B.
( c )
( D )
11
286The pendulum bob has a speed of ( 3 mathrm{m} / mathrm{s} )
at its lowest position. The pendulum is ( 0.5 mathrm{m} ) long. The speed of the bob, when
the bob makes an angle of ( 60^{circ} ) to the vertical will be ( left(boldsymbol{g}=mathbf{1 0 m} / boldsymbol{s}^{2}right) )
( A cdot 1 mathrm{m} / mathrm{s} )
B. ( 1.5 mathrm{m} / mathrm{s} )
( c cdot 3 m / s )
D. ( 2 mathrm{m} / mathrm{s} )
11
287Tension in the string in the mean position of an oscillating pendulum is:
A. Same as tension when it is not oscillating
B. Depend upon the time speedd
c. Less than tension when it is not oscillating
D. More than tension when it is not oscillating
11
288A particle moves along the ( x ) -axis
according to the equation ( boldsymbol{x}= )
10 ( sin 3(t) ). The amplitudes and
frequencies of component SHMs are
A ( cdot ) amplitude ( frac{30}{4}, frac{10}{4} ; ) frequencies ( frac{3}{2}, frac{1}{2} )
B. amplitude ( frac{30}{4}, frac{10}{4} ; ) frequencies ( frac{1}{2}, frac{3}{2} )
C. amplitude 10,( 10 ; ) frequencies ( frac{1}{2}, frac{1}{2} )
D. amplitude ( frac{30}{4}, 10 ; ) frequencies ( frac{3}{2}, 2 )
11
289When a mass ( m ) is connected
individually to two springs ( S_{1} ) and ( S_{2} ),
the oscillation frequencies are ( boldsymbol{v}_{1} ) and ( boldsymbol{v}_{2} )
If the same mass is attached to the two
springs as shown in figure, the
oscillation frequency would be:
A ( cdot v_{1}+v_{2} )
B. ( sqrt{v_{1}^{2}+v_{2}^{2}} )
( mathbf{c} cdotleft[frac{1}{v_{1}}+frac{1}{v_{2}}right]^{-1} )
D. ( sqrt{v_{1}^{2}-v_{2}^{2}} )
11
290Two S.H.M.’s are represented by the relations ( boldsymbol{x}=mathbf{4} sin (mathbf{8 0} boldsymbol{t}+boldsymbol{pi} / mathbf{2}) ) and ( boldsymbol{y}= )
( 2 cos (60 t+pi / 3) )
The ratio of their time periods is
A . 2:
B. 1:
c. 4: 3
D. 3:
11
291toppr
energy KE and time t is correctly
represented by
4
( B )
( c )
( D )
11
292A ball resting on a tray attached to a spring is made to oscillate vertically, such that the fixed end of the spring is attached to the ground. If the spring is compressed and let go, the ball will execute SHM until
A. the ball is in contact with the spring
B. the ball occasionally loses contact with the spring
c. the ball loses contact with the spring beyond the mean position
D. the ball loses contact with the spring beyond the extreme position
11
293Derive the equation for the kinetic energy and potential energy of a simple harmonic oscillator and show that the
total energy of a particle in simple harmonic motion constant at any point on its path.
11
294A particle of mass ( 10 g ) is undergoing SHM of amplitude ( 10 mathrm{cm} ) and period
( 0.1 s . ) The maximum value of force on
A ( .5 .6 N )
B. 2.75 N
c. ( 3.5 N )
D. ( 4 N )
11
295constant ( mathrm{k} ) are attached horizontally at the two ends of a uniform horizontally
rod ( A B ) of length ( ell ) and mass ( m ). The rod
is pivoted at its centre ‘O’ and can rotate
freely in horizontal plane. The other ends
of the two spring are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting
oscillation is:
( mathbf{A} cdot frac{1}{2 pi} sqrt{frac{6 k}{m}} )
B ( cdot frac{1}{2 pi} sqrt{frac{2 k}{m}} )
( mathbf{C} cdot frac{1}{2 pi} sqrt{frac{k}{m}} )
D. ( frac{1}{2 pi} sqrt{frac{3 k}{m}} )
11
296A plank with a body of mass ( m ) placed
on it starts moving straight up
according to the law ( y=a(1-cos omega t) )
where ( y ) is the displacement from the
initial position, ( omega=11 ) rad/s. Find the
minimum amplitude of oscillation of the plank at which the body starts falling behind the plank.
11
297What will be the displacement equation of the simple harmonic motion obtained by combining the motions? ( boldsymbol{x}_{1}=mathbf{2} sin boldsymbol{omega} boldsymbol{t}, quad boldsymbol{x}_{2}=boldsymbol{4} sin left(boldsymbol{omega} boldsymbol{t}+frac{boldsymbol{pi}}{boldsymbol{6}}right) )
and ( quad x_{3}=6 sin left(omega t+frac{pi}{3}right) )
A ( cdot x=10.25 sin (omega t+phi) )
B cdot ( x=10.25 sin (omega t-phi) )
C ( cdot x=11.25 sin (omega t+phi) )
D ( cdot x=11.25 sin (omega t-phi) )
11
298A solid cylinder of mass ( mathrm{m} ) is attached
to a horizontal spring with force constant k. The cylinder can roll without slipping along the horizontal plane. (See the accompanying figure.) Show that the center of mass of the cylinder executes simple harmonic motion with a period ( boldsymbol{T}=boldsymbol{2} boldsymbol{pi} sqrt{frac{boldsymbol{3} boldsymbol{m}}{boldsymbol{2} boldsymbol{k}}}, ) if displaced
from mean position.
11
299A wave is measured to have a frequency of ( 60 H z ). If its wavelength is ( 24 c m ) determine how fast it is moving.
( mathbf{A} cdot 24 m / s )
в. ( 10 mathrm{m} / mathrm{s} )
c. ( 12 m / s )
D. ( 14 mathrm{m} / mathrm{s} )
11
300One end of a rod of length ( L ) is fixed to a
point on the circumference of a wheel of radius R. The other end is sliding freely
along a straight channel passing
through the centre 0 of the wheel as
shown in the figure. The wheel is
rotating with a constant angular velocity ( omega ) about ( 0 . ) Taking ( T=frac{2 pi}{P omega} ) the
motion of the rod is?
A. Simple harmonic with a period of ( T )
B. Simple harmonic with a period of ( T / 2 )
c. Not simple harmonic but periodic with a period of ( T )
D. Not simple harmonic but periodic with a period of ( T / 2 )
11
301topp
grapillation Which one of the following
( T= ) time peric
:
11
302What is the minimum frequency of
sound waves needed to prepare
emulsion from two immiscible liquids?
11
303For a particle showing motion number
under the force ( F=-5(x-2)^{2} ), the
motion is
A. Translatory
B. Oscillatiory
c. sнm
D. All of these
11
304Time period of oscillation of a spring is
12s on earth. What shall be the time
period if it is taken to moon?
A . ( 6 s )
B. 12s
c. ( 36 s )
D. 72 s
11
305A simple harmonic motion has an amplitude ( A ) and time period T. Find the time required by it to travel directly from ( boldsymbol{x}=frac{boldsymbol{A}}{sqrt{mathbf{2}}} ) to ( boldsymbol{x}=boldsymbol{A} )11
306The time taken by a particle performing
SHM to pass from point ( A ) to ( B ) where
its velocities are same is 2 s. After
another ( 2 s ) it returns to ( B ). The ratio of
distance ( O B ) to its amplitude (where ( O )
is the mean position) is :
A. ( 1: sqrt{2} )
B . ( (sqrt{2}-1): 1 )
c. 1: 2
D. ( 1: 2 sqrt{2} )
11
307The actual frequency is
A. ( 5.645 mathrm{Hz} )
B. 7.685 Hz
c. ( 2.965 mathrm{Hz} )
D. 3.785 Нz
11
308( frac{k}{i} )11
309A particle oscillating under a force ( overline{boldsymbol{F}}= ) ( -k bar{x}-b bar{v} ) is a (k and b are constants)
A. simple harmonic oscillator
B. linear oscillator
c. damped oscillator
D. forced oscillator
11
310A particle of mass ( 0.1 k g ) executes ( S H M )
under a force ( boldsymbol{F}=(-10 x) N . ) Speed of
particle at mean position is ( 6 m / s ). Then amplitude of oscillations is
A. ( 0.6 m )
B. ( 0.2 m )
( c cdot 0.4 m )
D. ( 0.1 m )
11
311A particle is performing oscillations with acceleration ( a=8 pi^{2}-4 pi^{2} x )
where ( x ) is coordinate of the particle
w.r.t. the origin. The parameters are in
S.I. units. The particle is at rest at ( x=2 ) at ( t=0 . ) Find coordinates of the particle
w.r.t origin at any time.
A ( .4-2 cos 2 pi t )
B. ( 2-2 cos 2 pi t )
c. ( 4-4 cos 2 pi t )
D. ( 2+4 sin 2 pi t )
11
Based on the graphs, how does the
motion between the two objects differ?
Frequency
II. Angular Frequency
III. Period
IV. Amplitude
V. Phase Constant
A . I and II
B. I, II, and III
C. I and III
( D )
E. All of them (I – v )
11
313f a particle is executing SHM, with an amplitude ( A, ) the distance moved and the displacement of the body in a time equal to its period are
( A cdot 2 A, A )
B. ( 4 A, ),
( c cdot A, A )
D. ( 0,2 A )
11
314A bar magnet oscillates with a
frequency of10 oscillations per minute. When another bar magnet is placed on its axis at a small distance, it oscillates
at 14 oscillations per minute. Now, the second bar magnet is turned so that poles are instantaneous, keeping the location same. The new frequency of oscillation will be
( A cdot 2 ) vibrations/min
B. 4 vibrations/min
c. 10 vibrations/min
D. 14 vibrations/min
11
315A ball is dropped on a hard floor and no energy is being lost to the floor. The ball bounces back to the same position,
from where it was thrown. Is the ball
executing SHM
A. Yes, only for short displacements
B. Yes, for all displacements
c. No, for any kind of displacements
D. None of the above
11
316The angular frequency of small
oscillations of the system shown in the
figure is
A ( cdot sqrt{(K / 2 m)} )
B . ( sqrt{(2 K / m)} )
c. ( sqrt{(K / 4 m)} )
D. ( sqrt{(4 K / m)} )
11
317What is the phase difference
between acceleration and velocity of
a particle executing simple harmonic motion?
11
318( operatorname{In} operatorname{an} operatorname{SHM} x=operatorname{asin} omega t, ) the minimum
0.5 second what is the minimum time
A . ( 0.3 mathrm{s} )
B. ( 0.4 mathrm{s} )
( c cdot 0.2 s )
D. ( 0.1 mathrm{s} )
11
319Can a traingle have
A ( cdot 55^{circ}, 55^{circ} ) and ( 80^{circ} )
B . ( 33^{circ}, 74^{circ} ) and ( 73^{circ} )
c. ( 85^{circ}, 95^{circ} ) and ( 22^{circ} )
D. ( 25^{circ}, 95^{circ} ) and ( 32^{circ} )
11
320U is the PE of an oscillating particle and Fis the force acting on it at a given instant. Which of the following is true?
A ( cdot frac{U}{F}+x=0 )
B. ( frac{2 U}{F}+x=0 )
c. ( frac{F}{U}+x=0 )
D. ( frac{F}{2 U}+x=0 )
11
321The diagram in Fig. shows the displacement- time graph of a vibrating
body. Why is the amplitude of vibrations
11
322A block is executing SHM on a rough horizontal surface under the action of an external variable force.The force is
plotted against the position ( x ) of the
particle from the mean position
11
323The average kinetic energy of a simple harmonic oscillator with respect to
mean position will be:
A ( frac{k a^{2}}{6} )
в. ( frac{k a^{2}}{4} )
c. ( frac{k a^{2}}{3} )
D. ( frac{k a^{2}}{2} )
11
324The time taken by a particle performing ( boldsymbol{S H} boldsymbol{M} ) to pass from point ( boldsymbol{A} ) to ( boldsymbol{B} ) where its velocities are same is 2
seconds.After another 2 seconds it
returns to ( B ). The time period of oscillation is (in seconds)
A ( .2 s )
B. 8 s
( c cdot 6 s )
D. ( 4 s )
11
325The time period of the hour hand of a watch is
( A cdot 24 h )
B. 12 ( h )
( c cdot 1 h )
D. 1 min
11
326A transverse wave is described by the equation ( boldsymbol{y}=boldsymbol{y}_{0} sin 2 pileft(boldsymbol{f} boldsymbol{t}-frac{boldsymbol{pi}}{boldsymbol{lambda}}right) . ) The
maximum particle velocity is equal to four times the wave velocity if :
A ( cdot lambda=frac{pi y_{0}}{4} )
B. ( lambda=frac{pi y_{0}}{2} )
c. ( lambda=pi y_{0} )
D. ( lambda=2 pi y_{0} )
11
327Which of the following functions represent a simple harmonic motion?
( mathbf{A} cdot sin omega t-cos omega t )
B. ( sin ^{2} omega t )
( mathbf{c} cdot sin omega t+sin ^{2} omega t )
D. ( sin omega t-sin ^{2} omega t )
11
328Assertion: If a block is in SHM, and a
new constant force acts in the direction
of change, the mean position may change. Reason :In SHM only variable forces
should act on the body, for example spring force.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct and Reason is not the correct explanation for Assertion
c. Assertion is correct and Reason is incorrect
D. Assertion is incorrect and Reason is correct
11
329Assertion : Every periodic motion is not simple harmonic motion.
Reason: The motion governed by the
force law
( boldsymbol{F}=-boldsymbol{k} boldsymbol{x} ) is simple harmonic.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false.
D. If both assertion and reason are false
11
330Two SHMs are given by ( boldsymbol{Y}_{mathbf{1}}= )
( A sin left(frac{pi}{2} t+phiright) ) and ( Y_{2}=B sin left(frac{2 pi t}{3} t+right. )
( phi ). The phase difference between these
two after ‘1’ sec is
A . ( pi )
в. ( frac{pi}{2} )
c. ( frac{pi}{4} )
D.
11
331A simple harmonic oscillator of angular
frequency 2 rad ( s^{-1} ) is acted upon by an
external force ( F=sin t N . ) If the
oscillator is at rest in its equilibrium position at ( t=0, ) its position at later times is proportional to
A ( cdot sin t+frac{1}{2} cos 2 t )
B cdot ( operatorname{cost}-frac{1}{2} sin 2 t )
( mathrm{c} cdot operatorname{sint}-frac{1}{2} sin 2 t )
D. ( sin t+frac{1}{2} sin 2 t )
11
332A particle executes SHM with a time period of 10 secs. At what times will the velocity of the particle be maximum, if at ( t=0, ) the particle starts from ( x=-A )
B. (0,10)
c. (5,10)
D. (2.5,7.5)
11
performing SHM with an amplitude of
1 ( m ). When the cannon reaches ( x= )
( frac{sqrt{3}}{2} m ) from the equilibrium
moving along +x direction, a bullet of ( frac{1}{2} k g ) is suddenly fired from it with ( a )
velocity of ( 20 m / s ) relative to the ground. What will be the new amplitude of the
cannon?
( ^{A} cdot frac{sqrt{3}}{2} )
B. ( frac{sqrt{5}}{2} )
c. ( frac{sqrt{7}}{2} )
D. ( frac{sqrt{11}}{2} )
11
334Average Kinetic energy in one time
period in an SHM is (Where ( m, omega ) and ( y_{0} )
are mass of particle, angular velocity and maximum displacement respectively)
( ^{A} cdot frac{m omega^{2} y_{0}^{2}}{2} )
B . ( m omega^{2} y_{0}^{2} )
c. ( frac{m omega^{2} y_{0}^{2}}{3} )
D. ( frac{m omega^{2} y_{0}^{2}}{4} )
11
335Two particles move parallel to ( x- ) axis
about the origin with same amplitude
( a^{prime} ) and frequency ( omega . ) At a certain instant they are found at a distance ( a / 3 ) from
the origin on opposite sides but their velocities are in the same direction.
What is the phase difference between the two?
A ( cdot cos ^{-1} frac{7}{9} )
B. ( cos ^{-1} frac{5}{9} )
( ^{mathbf{C}} cdot cos ^{-1} frac{4}{9} )
D. ( cos ^{-1} frac{1}{9} )
11
336The time period of the variation of potential energy of a particle executing ( boldsymbol{S H} boldsymbol{M} ) with period ( boldsymbol{T} ) is
( mathbf{A} cdot T / 4 )
в. ( T )
c. ( 2 T )
D. ( T / 2 )
E . ( T / 3 )
11
337Two particles ( A ) and ( B ) are revolving on two circles with time periods 4 second and 6 second respectively. Time period of particle A with respect to B will be
A. 6 seconds
B. 12 seconds
c. 18 seconds
D. 24 seconds
11
338A particle executing SHM of amplitude ( 4 c m ) and ( T=4 s . ) The time taken by it to
move from positive extreme position to half the amplitude is
A . ( 1 s )
B. ( frac{1}{3} s )
c. ( frac{2}{3} )
D. ( sqrt{frac{3}{2}} s )
11
339A particle starts performing simple
harmonic motion. Its amplitude is ( A ). At one time its speed is half that of the maximum speed. At this moment the displacement is:
A ( cdot frac{sqrt{2} A}{3} )
B. ( frac{sqrt{3} A}{2} )
c. ( frac{2 A}{sqrt{2}} )
D. ( frac{3 A}{sqrt{2}} )
11
340A body oscillates with SHM according to
the equation ( boldsymbol{x}=mathbf{5 . 0} cos (2 pi t+boldsymbol{pi}) . ) At
time ( t=1.5 s, ) its displacement, speed
and acceleration respectively is:
B . ( 5,0,-20 pi^{2} )
c. ( 2.5,+20 pi, 0 )
D. ( -5.0,+5 pi,-10 pi^{2} )
11
341The equation of motion of a body in
S.H.M is ( boldsymbol{x}=mathbf{4} sin left(boldsymbol{pi} boldsymbol{t}+frac{pi}{3}right) . ) The
frequency, per minute, of the motion is
11
342The potential energy of a simple
pendulum will be maximum when it is-
A. At the turning points of oscillations
B. At the equilibrium
C. In between the above two cases
D. At any position, it has always a fixed value
11
343A string fixed at both ends, oscillate in
( 4^{t h} ) harmonic. The displacement of a particle of string is given as:
( boldsymbol{Y}=boldsymbol{2} boldsymbol{A} sin (boldsymbol{5} boldsymbol{pi} boldsymbol{x}) cos (boldsymbol{1} boldsymbol{0} boldsymbol{0} boldsymbol{pi} boldsymbol{t}) . ) Then find
the length of the string?
( mathbf{A} cdot 80 mathrm{cm} )
B. 100 ст
( mathbf{c} .60 mathrm{cm} )
D. ( 120 mathrm{cm} )
11
344The displacement ( y ) of a executing Periodic motion is given by ( y=4 cos ^{2}left(frac{1}{2} tright) sin (1000 t) )
This expression may be considered to be a result of the superposition of independent harmonic motions.
A. two
B. three
c. four
D. five
11
345A particle performs SHM with period and amplitude A. The mean velocity of the particle averaged over quarter oscillation, starting from right extreme position is
( mathbf{A} cdot mathbf{0} )
в. ( frac{2 A}{T} )
c. ( frac{4 A}{T} )
D. ( frac{3 A}{T} )
11
346A particle suspended from a fixed point, by a light inextensible thread of length is projected horizontally from its lowest position with velocity ( sqrt{frac{mathbf{7 g L}}{mathbf{2}}} . ) The thread will slack after swinging through
an angle ( theta, ) such that ( theta ) equal
A ( .30^{circ} )
B. ( 135^{circ} )
( c cdot 120^{circ} )
D. ( 150^{circ} )
11
347The differential equation representing the SHM of a particule is ( frac{mathbf{9} d^{2} boldsymbol{y}}{boldsymbol{d} boldsymbol{t}^{2}}+boldsymbol{4} boldsymbol{Y}= )
0.The time period of the particle is fiven
by
A ( frac{pi}{3} sec )
в. ( pi ) sec
( ^{mathrm{c}} cdot frac{2 pi}{3} s e c )
D. ( 3 pi s e c )
11
348Two blocks each of mass m is
connected to the spring of spring constant ( mathrm{k} ) as shown in the figure.
If the blocks are displaced slightly in opposite directions and released, they
will execute simple harmonic motion.
The time period of oscillation is
A. ( 2 pi sqrt{frac{m}{k}} )
В ( .2 pi sqrt{frac{m}{2 k}} )
( mathbf{c} cdot 2 pi sqrt{frac{m}{4 k}} )
D. ( 2 pi sqrt{frac{2 m}{k}} )
11
349When a particle executing SHM
oscillates with a frequency’ ( omega^{prime}, ) then the kinetic energy of the particle
A. Changes periodically with a frequency of ‘ ( omega^{prime} )
B. Changes periodically with a frequency of ‘2 ( omega ) ‘
C . changes periodically with a frequency of ( ^{prime} frac{omega}{2} )
D. Remains constant
11
350The displacement of particle in SHM in one time period is
A . zero
B. a
c. ( 2 a )
D. 42
11
351ILLUSTRATION 33.7 For different L (meter)
values of L, we get different values
of T. The curve between L v/s T is
shown. Estimate g from this curve.
(Take it = 10)
0.49
> 1452)
11
352The displacement of the particle varies with time ( x=12 sin omega t-16 sin ^{3} omega t . ) If its
motion is SHM, then maximum
acceleration is
A ( cdot 12 omega^{2} )
B. 36 ( omega^{2} )
c. ( 144 omega^{2} )
D. ( sqrt{192} omega^{2} )
11
353The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the
string. The angular amplitude of the pendulum is?
A ( cdot 90^{circ} )
B. ( 60^{circ} )
( c cdot 45^{circ} )
D. ( 30^{circ} )
11
354Assertion
In ( S H M, ) acceleration is always
directed towards the mean position.
Reason
( ln S H M, ) the body has to stop
momentary at the extreme position and move back to mean position.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
355The phase space diagram for simple
Momentum harmonic motion is a circle
centered at the origin. In the figure, the
two circles represent the same oscillator but for different initia
conditions, and ( E_{1} ) and ( E_{2} ) are the total
mechanical energies respectively. Then:
( mathbf{A} cdot E_{1}=sqrt{2} E_{2} )
( mathbf{B} cdot E_{1}=2 E_{2} )
( mathbf{c} cdot E_{1}=4 E_{2} )
( mathbf{D} cdot E_{1}=16 E_{2} )
11
356A mass of ( 2.0 mathrm{kg} ) is put on a flat pan attached to a vertical spring fixed on the ground as shown in the figure. The mass of the spring and the pan is negligible. When pressed slightly and
released the mass executes a simple harmonic motion. The spring constant is ( 200 mathrm{N} / mathrm{m} ). What should be the
minimum amplitude of the motion, so
that the mass gets detached from the
pan?
(Take ( left.g=10 m / s^{2}right) )
A. ( 8.0 mathrm{cm} )
B. 10.0 ( mathrm{cm} )
c. Any values less than ( 12.0 mathrm{cm} )
D. 4.0 ( mathrm{cm} )
11
357A particle executes linear simple harmonic motion with an amplitude of ( 3 mathrm{cm} . ) When the particle is at ( 2 mathrm{cm} ) from the mean position, the magnitude of its velocity is equal to that of its acceleration. Then its time period in seconds is
( ^{mathrm{A}} cdot frac{sqrt{5}}{pi} )
в. ( frac{sqrt{5}}{2 pi} )
c. ( frac{4 pi}{sqrt{5} pi} )
D. ( frac{2 pi}{sqrt{3}} )
11
358A particle executes simple harmonic
motion between ( boldsymbol{x}=-boldsymbol{A} boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{x}=+boldsymbol{A} )
The time taken for it to go from 0 to ( A / 2 )
to ( A ) is ( T_{2} ). Then
A ( cdot T_{1}T_{2} )
c. ( T_{1}=T_{2} )
D. ( T_{1}=2 T_{2} )
11
359A uniform disc of mass ( M ) and radius ( R )
is suspended in vertical plane from a point on its periphery. Its time period of oscillation is
A ( cdot 2 pi sqrt{frac{3 R}{g}} )
в. ( 2 pi sqrt{frac{R}{3 g}} )
( ^{mathrm{c}} cdot_{2 pi} sqrt{frac{2 R}{3 g}} )
D. ( 2 pi sqrt{frac{3 R}{2 g}} )
11
360Velocity at mean position of a particle executing SHM is ( v ), then velocity of the particle at a distance equal to half of the amplitude is
( A cdot frac{sqrt{3}}{2} v )
B. ( frac{2}{sqrt{3}} v )
( c cdot 2 v )
D. ( v )
11
361To show that a simple pendulum executing a simple harmonic motion it
is necessary to assume that
A. length of the pendulum is small.
B. mass of the pendulum is small
c. acceleration due to gravity is small.
D. amplitude of the oscillation is small.
11
362What to you understand by free
vibrations of a body?
11
363The angular frequency of the damped oscillator is given by ( omega=sqrt{left(frac{k}{m}-frac{r^{2}}{4 m^{2}}right)} ) where ( k ) is the
spring constant, ( m ) is the mass of the oscillator and ( r ) is the damping constant. If the ratio ( frac{r^{2}}{m k} ) is ( 80 %, ) the change in time period compared to the undamped oscillator is approximately
as follows:
A. increases by 8%
B. decreases by 8%
C. increases by ( 1 % )
D. decreases by 1%
11
364The time period of a particle executing SHM is ( 8 s . ) At ( t=0, ) it is at mean
position. If ( A ) is the amplitude of particle, then the distance travelled by particle (in second) is?
A ( cdot sqrt{2} A )
B ( cdotleft(1-frac{1}{sqrt{2}}right) )
c. ( 2 A )
D. ( frac{A}{sqrt{2}} )
11
365The pendulum of a bob undergoes SHM with an amplitude A is given by the equation ( boldsymbol{y}=boldsymbol{A} boldsymbol{s} boldsymbol{i n} boldsymbol{omega} boldsymbol{t} . ) The
corresponding angular SHM equation can be written as
A ( cdot theta=phi cos (omega t) )
в. ( theta=phi sin (omega t) )
c. ( theta=phi tan (omega t) )
D. ( theta=phi(omega t) )
11
366A particle is performing SHM of amplitude “A” and time period “T”. Find the time taken by the particle to go from 0 to ( A / sqrt{2} )
A . T/12
B. ( T / sqrt{2} )
c. ( pi / 6 )
D. ( t / 4 )
11
367A body executes S.H.M. under the action of a force ( boldsymbol{F}_{1} ) with a time period ( mathbf{4} / mathbf{5} )
seconds. If the force is changed to ( boldsymbol{F}_{2}, ) it
executes S.H.M. with a time period ( 3 / 5 )
seconds. If both the forces ( F_{1} ) and ( F_{2} ) act
simultaneously in the same direction on the body, then its time period in seconds is:
A . ( 12 / 25 )
в. ( 24 / 25 )
c. ( 25 / 24 )
D. 25/12
11
368The velocity of a particle executing a
simple harmonic motion is ( 13 m s^{-1} )
when its distance from the equilibrium position ( (Q) ) is ( 3 m ) and its velocity is
( 12 m s^{-1}, ) when it is ( 5 m ) away from ( Q )
The frequency of the simple harmonic motion is:
( mathbf{A} cdot frac{5 pi}{8} )
В. ( frac{5}{8 pi} )
c. ( frac{8 pi}{5} )
D. ( frac{8}{5 pi} )
11
369The acceleration (a) of SHM at mean
position is :
A. zero
B. ( propto x )
( c cdot propto x^{2} )
D. None of these
11
370If the maximum velocity of a particle in
SHM is ( v_{0}, ) then its velocity at half the amplitude from position of rest will be :
A ( cdot v_{0} / 2 )
B. ( v_{0} )
c. ( v_{o} sqrt{3} / 2 )
D . ( v_{0} sqrt{3} / 4 )
11
371A simple harmonic motion has an
amplitude ( A ) and time period ( T . ) The
time required by it to travel ( x=A ) to
( boldsymbol{x}=frac{boldsymbol{A}}{2} ) is:
A. ( T / 6 )
в. ( T / 4 )
c. ( T / 3 )
D. ( T / 2 )
11
372The equilibrium position of the particle
is
A. ( x=4 )
B. ( x=6 )
( c cdot x=2 )
D. x = 3
11
373A particle executes SHM with a frequency f and its amplitude is A. If the frequency is doubled, the amplitude will be
( A cdot A / 2 )
B. A
c. ( 2 A )
D. A/4
11
374The time period of a simple harmonic motion is ( 8 s . ) At ( t=0, ) it is at its
equilibrium position. The ratio of distances transversed by it in the first and second seconds is:
A ( cdot frac{1}{sqrt{2}} )
в. ( frac{1}{sqrt{2}-1} )
c. ( frac{1}{sqrt{3}} )
D. ( frac{1}{2} )
11
375In which of the following is the energy loss maximum?
A. sonometer
B. tuning fork
c. thin tube
11
376A smooth inclined plane having angle of
inclination ( 30^{circ} ) with horizontal has a
mass 2.5 kg held by a sprang which is fixed at the upper end as shown in figure. If the mass is taken ( 2.5 mathrm{cm} ) up along the surface of the inclined plane,
the tension in the spring reduces to zero
If the mass is then released, the angular frequency of oscillation in radian per second is:
A. 0.707
В. 7.07
c. 1.414
D. 14.14
11
377The period of oscillation of a simple
pendulum of constant length is independent of
( A ). size of the bob
B. shape of the bob
c. mass of bob
D. all of these
11
378The amplitude of vibration of oscillating particle goes on decreasing because it is opposed by…
A. resistive force of the medium
B. resistive force by source oscillator
c. resistive force by observer
D. resistive force produced itself
11
379The displacement ( x ) of a particle in
motion is given in terms of time by ( x(x- )
4) ( =1-5 cos omega t )
A. The particle executes SHM
B. The particle executes oscillatory motion which is not SHM
C. motion of the particle is neither oscillator; nor simple harmonic
D. The particle is not acted upon by a force when it is at ( x ) ( =4 )
11
380Two masses ( m_{1} ) and ( m_{2} ) are connected
to a spring of spring constant ( K ) at two
ends. The spring is compressed by ( y ) and released. The distance moved by
( m_{1} ) before it comes to a stop for the first time is
A. ( frac{m_{1} y}{m_{1}+m_{2}} )
в. ( frac{m_{2} y}{m_{1}+m_{2}} )
c. ( frac{2 m_{1} y}{m_{1}+m_{2}} )
D. ( frac{2 m_{2} y}{m_{1}+m_{2}} )
11
381A block tied between two identical
springs is in equilibrium. If upper spring is cut, then the acceleration of
the block just after the cut is ( 6 m s^{-2} )
Now if instead of upper string lower spring is cut, then the acceleration of
the block just after the cut will be
(Take ( left.g=10 m / s^{2}right) )
A ( .1 .25 mathrm{ms}^{-2} )
B. ( 4 m s^{-2} )
( mathrm{c} cdot 10 mathrm{ms}^{-2} )
D. ( 2.5 mathrm{ms}^{-2} )
11
382Out of the following functions representing motion of a particle which
represents ( boldsymbol{S H} boldsymbol{M} ) ?
(A) ( y=sin omega t-cos omega t )
(B) ( y=sin ^{3} omega t )
(C) ( y=5 cos left(frac{3 pi}{4}-3 omega tright) )
(D) ( boldsymbol{y}=mathbf{1}+boldsymbol{omega} boldsymbol{t}+boldsymbol{omega}^{2} boldsymbol{t}^{2} )
A. Only ( (A) ) and ( (B) )
B. only ( (A) )
c. only ( (D) ) does not represent ( S H M )
D. only ( (A) ) and ( (C) )
11
383A student writes the equation of an angular ( mathrm{SHM} ) as ( boldsymbol{pi} / mathbf{3}=boldsymbol{pi} / mathbf{6} sin (boldsymbol{omega} boldsymbol{t}) . ) Is
this correct?
A. This equation is correct as it is of the form ( theta= ) ( phi sin (omega t) )
B. This equation is incorrect as instantaneous angular displacement is more than the angular amplitude
C. This equation is incorrect as the equation lacks a phase factor
D. This equation is correct since the SHM has a sin factor in it
11
384Which of the following exhibit simple harmonic motion?
I. A pendulum
II. A mass attached to a spring
III. A ball bouncing up and down, in the absence of friction
A. I only
B. II only
c. ॥ only
D. I and II only
E . ।, ॥।, and III
11
385A pendulum suspended from the ceiling of a train has a time period T when the train is at rest. When the train is
accelerating with a uniform acceleration, the time period will
( A ). increase
B. decrease
c. become infinite
D. remain unaffected
11
386The graphs in figure show that a quantity y varies with displacement d in a system undergoing simple harmonic motion. The unbalanced force acting on the system.
( A )
B. I
( c )
( D . ) iv
11
387A 0.5 kg body performs simple harmonic motion with a frequency of 2
( mathrm{Hz} ) and an amplitude of ( 8 mathrm{mm} ). Find the
maximum velocity of the body, its maximum acceleration and the
maximum restoring force to which the body is subjected.
11
388The displacement of a particle executing simple harmonic motion is given by equation ( y=0.3 sin 20 pi(t+0.05) )
where time ( t ) is in second and
displacement y is in metre. calculate the values of amplitude, time period initial phase and initial displacement of the particle
11
389The amplitude and time period of a particle of mass ( 0.1 mathrm{kg} ) executing simple harmonic motion are ( 1 mathrm{m} ) and ( 6.28 mathrm{s} ) respectively. Then its (i)angular frequency,
(ii) acceleration at
a displacement of ( 0.5 mathrm{m} ) are respectively
A ( cdot 1 mathrm{rad} / mathrm{s}, 0.5 mathrm{m} / mathrm{s}^{2} )
c. ( 0.5 mathrm{rad} / mathrm{s}, 0.5 mathrm{m} / mathrm{s}^{2} )
D. 1 rad/s, ( 1 mathrm{m} / mathrm{s}^{2} )
11
390A particle execute S.H.M from the mean position. its amplitude is ( A ), its time period is “T.’ At what displacement,its speed is half of its maximum speed.
A ( cdot frac{sqrt{3} A}{2} )
в. ( frac{sqrt{2}}{3} A )
c. ( frac{2 A}{sqrt{3}} )
D. ( frac{3 A}{sqrt{A}} )
11
391The graph shows the variation in
displacement with time for an object
moving with simple harmonic motion. What is the maximum
acceleration of the object?
A . 10
B. 0.99
( c .0 .44 )
D. none of the above
11
392A particle is executing SHM with amplitude A and has maximum
velocity ( V_{0} . ) Its speed at displacement A/2 will be
11
393The displacement of a particle varies
according to the relation ( boldsymbol{y}= )
( 4(cos pi t+sin pi t) . ) The amplitude of the
particle is:
A. 8 units
B. 2 units
c. 4 units
D. ( 4 sqrt{2} ) units
11
394A body executing ( S . H . M . ) along a
straight line has a velocity of ( 3 m s^{-1} )
when it is at a distance of 4 m from its
mean position and ( 4 m s^{-1} ) when it is at
a distance of ( 3 m ) from its mean
position. Its angular frequency and amplitude are:
A ( cdot 2 ) rad ( s^{-1} ) & ( 5 m )
B. 1 rad ( s^{-1} ) & ( 10 m )
c. 2 rad ( s^{-1} ) & ( 10 m )
D. 1 rad ( s^{-1} ) & ( 5 m )
11
395In SHM match the following
Column I
a) Maximum velocity
e) ( 1 / 2 mathrm{M} )
( omega^{2} A^{2} )
b) Maximum acceleration
f) ( 1 / 4 mathrm{M} )
( omega^{2} A^{2} )
c) Maximum Force
g) ( A omega )
d) Maximum total energy
h) ( omega^{2} A )
¡) ( boldsymbol{m} boldsymbol{omega}^{2} boldsymbol{A} )
A. a-g, b-h, c-i, d-e
B. a-h, b-g, c-i, d-e
c. ( a-g, b-h, c-f, d-e )
D. a-g, b-i, c-h, d-f
11
396A particle executes SHM about a point
other than ( x=0 ) as shown in the graph
Choose a CORRECT option(s)
This question has multiple correct options
A. Amplitude is equal to ( 4 m )
B. Equilibrium position is at ( x=0 )
C. Equilibrium position is at ( x=2 m )
Angular frequency ( frac{2 pi}{3} )
11
397A particle of mass ( mathrm{m} ) is performing simple harmonic motion along line AB with amplitude 2 a with centre of oscillation as ( 0 . ) At time ( t=0 ) particle is
at point ( C(O C=a) ) and is moving towards B with velocity ( boldsymbol{v}=boldsymbol{a} sqrt{mathbf{3}} mathrm{m} / mathrm{s} )
The equation of motion can be given by This question has multiple correct options
A. ( x=2 a(sin t+sqrt{3} cos t) )
B cdot ( x=2 a sin left(t+frac{pi}{6}right) )
c. ( x=a(sin t+sqrt{3} cos t) )
D. ( x=a(sqrt{3} sin t+cos t) )
11
398A particle moves in a circular path with
a uniform speed. Its motion is:
A. Periodic
B. Oscillatory
c. simple harmonic
D. Angular simple harmonic
11
399Which of the following quantities is
non-zero at the mean position for a
particle executing SHM?
( A cdot ) force
B. acceleration
c. velocity
D. displacement
11
400The maximum speed of a body vibrating
under S.H.M. with time period of ( pi / 4 ) s
amplitude ( 7 mathrm{cm} ) is
( A cdot 488 mathrm{cm} / mathrm{s} )
B. ( 56 mathrm{cm} / mathrm{s} )
c. ( 38.5 mathrm{cm} / mathrm{s} )
D. ( 5.5 mathrm{cm} / mathrm{s} )
11
401A particle starts from a point ( mathrm{P} ) at ( mathrm{a} ) distance of A/2 from the mean position
0 and travels towards left as shown in
the figure. If the time period of ( mathrm{SHM} ) executed about 0 is ( mathrm{T} ) and amplitude ( mathrm{A} )
then the equation of the motion of
particle is:
This question has multiple correct options
A ( cdot x=A sin left(frac{2 pi}{T} t+frac{pi}{6}right) )
B. ( x=A sin left(frac{2 pi}{T} t+frac{5 pi}{6}right) )
c. ( x=A cos left(frac{2 pi}{T} t+frac{pi}{6}right) )
D. ( x=A cos left(frac{2 pi}{T} t+frac{pi}{3}right) )
11
402A system of springs with their springs constants are as shown in figure. The
frequency of oscillation of the mass ( m )
will be (assuming the springs to be massless
A ( cdot frac{1}{2 pi} sqrt{frac{k_{1} k_{2}left(k_{3}+k_{4}right)}{left[left(k_{1}+k_{2}right)+left(k_{3}+k_{4}right)+k_{1} k_{4}right] m}} )
B ( cdot frac{I}{2 pi} sqrt{frac{k_{1} k_{2}left(k_{3}+k_{4}right)}{left[left(k_{1}+k_{2}right)+left(k_{3}+k_{4}right)+k_{1} k_{2}right] m}} )
c. ( frac{1}{2 pi} sqrt{frac{k_{1} k_{2}left(k_{3}+k_{4}right)}{left[left(k_{1}+k_{2}right)+left(k_{3}+k_{4}right)+k_{1} k_{2}right] m}} )
D ( frac{1}{2 pi} sqrt{frac{left(k_{1}+k_{2}right)+left(k_{3}+k_{4}right)+k_{1} k_{2}}{left[left(k_{1}+k_{2}right)+left(k_{3}+k_{4}right)+k_{1} k_{2}right] m}} )
11
connected to a fixed vertical wall and
the other end has a block of mass ( mathrm{m} )
initially at rest on a smooth horizontal
surface. The spring is initially in natural length. Now a horizontal force F acts on the block as shown. Then the maximum
extension in spring is equal to the maximum compression in the spring.
Reason

To compress and to expand an ideal unstretched spring by equal amount, same work is to be done on the spring.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct

11
404Fill in the blank
A point source emits sound equally in all direction in a non-absorbing
medium. Two point ( P ) and ( Q ) are at a
distance of ( 9 m ) and ( 25 m ) respectively
from the source. The ratio of the
amplitudes of the waves at ( P ) and ( Q ) is..
11
405A particle is executing simple harmonic motion with an amplitude ( A ) and time
period ( T . ) The displacement of the
particles after ( 2 T ) period from its initial position is
A . ( A )
в. ( 4 A )
c. ( 8 A )
D. zero
11
406A stone tied at the end of string ( 80 mathrm{cm} ) long is whirled in a horizontal circle
with a constant speed. If the stone makes 25 revolutions in 14 s, what is
the magnitude of acceleration of the
stone?
A ( .90 m s^{-2} )
B. ( 100 mathrm{ms}^{-2} )
( mathbf{c} cdot 110 m s^{-2} )
D. ( 120 mathrm{ms}^{-2} )
11
407Starting from an origin, a body oscillates simple harmonically with a period of ( 2 s . ) After what time will its
kinetic energy be ( 75 % ) of the total
energy?
A . ( 1 / 6 s )
B. ( 1 / 12 s )
( mathrm{c} cdot 1 / 3 s )
D. ( 1 / 4 s )
11
408Draw a sketch showing the displacement of a body executing damped vibrations against time.11
409( boldsymbol{E} ) is kinetic energy of a simple harmonic oscillator at its mean
position. The phase angle from mean position at which its kinetic energy is ( boldsymbol{E} / 2 ) is :
A . ( pi / 5 ) rad
в. ( pi / 4 ) rad
c. ( pi / 3 ) rad
D. None of the above
11
410The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is:-
A. zero
в. ( 0.5 pi )
( c )
D. ( 0.707 pi )
11
411A particle performing linear simple
harmonic motion has maximum
velocity ( 25 mathrm{cm} / mathrm{s} ) and maximum
acceleration of ( 100 mathrm{cm} / mathrm{s}^{2} ). Find the amplitude and period of oscillation. ( (boldsymbol{pi}=mathbf{3 . 1 4 2}) )
11
412A particle executes SHM whose instantaneous displacement is given by ( boldsymbol{x}=boldsymbol{A} cos (boldsymbol{omega} boldsymbol{t}+boldsymbol{pi} / 2) . ) What will be its
acceleration at ( t=T / 4 )
( mathbf{A} cdot a=0 )
B . ( a=2 omega^{2} A )
( mathbf{c} cdot a=omega^{2} A )
D. ( a=omega^{2} A / 2 )
11
413A steamer moves with velocity ( 3 mathrm{km} / mathrm{h} ) in and against the direction of river water whose velocity is ( 2 mathrm{km} / mathrm{h} ). Calculate the total time for the total journey if the boat travels ( 2 mathrm{km} ) in the direction of a stream
and then back to its place:
A. 2 hrs
B. 2.5 hrs
c. 2.4 hrs
D. 3 hrs
11
414Acceleration-displacement graph of a
particle executing SHM is as shown in
the figure. The time period of oscillation is (in sec)
A ( cdot frac{pi}{2} )
B. ( 2 pi )
( c )
D. ( frac{pi}{4} )
11
415A plot of ( f ) vs ( (1 / T) ) gives
A. a straight line passing through the origin
B. a straight line parallel to frequency axis
C. a straight line perpendicular to frequency axis
D. a straight line having an intercept along frequency axis
11
416The unit ‘hertz’ is same as.
A. second
B. Second( ^{-1} )
c. Metre
D. metre ( ^{-1} )
11
417The displacement of a particle undergoing ( S H M ) of time period ( T ) is
given by ( boldsymbol{x}(boldsymbol{t})=boldsymbol{x}_{boldsymbol{m}} cos (boldsymbol{omega} boldsymbol{t}-boldsymbol{phi}) . ) The
particle is at ( boldsymbol{x}=-boldsymbol{x}_{m} ) at time ( boldsymbol{t}=mathbf{0} )
The particle is at ( boldsymbol{x}=+boldsymbol{x}_{boldsymbol{m}} ) when
( mathbf{A} cdot t=0.25 T )
в. ( t=0.50 T )
c. ( t=0.75 T )
D. ( t=1.00 T )
11
418Apparent weight at bottom most line is
A . 2 mg
в. ( m g )
( mathrm{c} .3 mathrm{mg} )
D. ( 4 mathrm{mg} )
11
419Two particle performed simple harmonic motion of same frequency an
amplitude is same and is equal to ( boldsymbol{A} )
and their time period is ( T . ) If at ( t=0 )
separation is maximum and is ( A ), their separation at ( t=frac{T}{12} ) is:-
A ( cdot quad A frac{sqrt{3}}{2} )
B. ( A )
c. ( frac{A}{sqrt{2}} )
D. ( frac{A}{2} )
11
420A body is executing simple harmonic motion of amplitude ( a ) and period ( T )
about the equilibrium position ( boldsymbol{x}=mathbf{0} )
Large numbers of snapshots are taken
at random of this body in motion. The probability of the body being found in a
very small interval ( boldsymbol{x} ) to ( boldsymbol{x}+|boldsymbol{d} boldsymbol{x}| ) is
highest at
A. ( x=pm a )
В. ( x=pm a / 2 )
c. ( x=0 )
D. ( x=pm a / sqrt{2} )
11
421A body executes simple harmonic motion. At a displacement ( x ), its
potential energy is ( U_{1} . ) At a displacement ( y, ) its potential energy is
( U_{2} . ) What is the potential energy of the body at a displacement ( (x+y) ? )
A. ( U_{1}+U_{2} )
В ( cdot(sqrt{U_{1}}+sqrt{U_{2}})^{2} )
c. ( sqrt{U_{1}^{2}+U_{2}^{2}} )
D. ( sqrt{U_{1} U_{2}} )
11
422A particle executes simple harmonic motion between ( x=-A ) and ( x=+A ).The
time taken by it to go from 0 to A /2 is ( T )
1 and to go from ( A / 2 ) to ( A ) is ( T_{2} . ) Then
( A cdot T_{1}T_{2} )
( mathrm{c} cdot mathrm{T}_{1}=mathrm{T}_{2} )
D. ( mathrm{T}_{1}=2 mathrm{T}_{2} )
11
423Frequency of oscillation of a body is
6 ( H z ) when force ( F_{1} ) is applied and
( 8 H z ) when ( F_{2} ) is applied. If both forces
( F_{1} & F_{2} ) are applied together then, the frequency of oscillation is :
( mathbf{A} cdot 14 H z )
в. ( 2 mathrm{Hz} )
c. ( 10 H z )
D. ( 10 sqrt{2} mathrm{Hz} )
11
424Fill in the blank
A cylindrical resonance tube open at both ends fundamental frequency ( boldsymbol{F} ) in
the air. Half-length of the tube is dipped vertically in the water. The fundamental frequency to the air column now is
11
425Two springs of force constants ( mathbf{1 0 0 0} N / boldsymbol{m} ) and ( mathbf{2 0 0 0} boldsymbol{N} / boldsymbol{m} ) are
stretched by same force. The ratio of their respective potential energies is
A .2: 1
B. 1: 2
c. 4: 1
D. 1: 4
11
426A body undergoing ( S H M ) about the
origin has its equation is given by ( boldsymbol{x}= ) ( 0.2 cos 5 pi t . ) Find its average speed in
( boldsymbol{m} / boldsymbol{s} ) from ( boldsymbol{t}=mathbf{0} ) to ( boldsymbol{t}=mathbf{0 . 7} boldsymbol{s e c} )
11
427Find force constant for small oscillation
around equilibrium:
A. ( 580 N m^{-1} )
B. ( 58 N m^{-1} )
c. ( 400 N m^{-1} )
D. none of these
11
428Displacement versus time curve for a
particle executing SHM is as shown in
figure.
At what points the velocity of the
particle is zero?
( A cdot A, C, E )
B. В, D, F
( c cdot A, D, F )
D. ( mathrm{C}, mathrm{E}, mathrm{F} )
11
429When a particle oscillates simple harmonically, its kinetic energy varies periodically. If frequency of the particle
is ( n, ) the frequency of the kinetic energy
is:
A ( cdot n / 2 )
в. ( n )
( c cdot 2 n )
D. ( 4 n )
11
430An unhappy mouse of mass ( m_{0}, ) moving on the end of a spring of spring constant p is acted upon by a damping force
( F_{x}=-b v_{x} . ) For what value of ( b ) the
motion is critically damped?
A ( cdot b=sqrt{frac{p}{m_{0}}} )
B. ( b=2 sqrt{p m_{0}} )
( ^{mathrm{c}}_{b}=sqrt{frac{p^{2}}{2 m_{0}}} )
D. ( b=sqrt{frac{p}{2 m_{0}}} )
11
431The amplitude of a particle executing
SHM about 0 is ( 10 mathrm{cm} . ) Then:
A. when the KE is 0.64 times of its maximum KE, its displacement is 6 cm from 0
B. its speed is half the maximum speed when its displacement is half the maximum displacement
( c . ) Both
(a) and
(b) are correct
D. Both (a) and
(b) are wrong
11
432A particle of mass ( m ) is executing
oscillations about the origin on the ( x- ) axis. It’s potential energy is ( boldsymbol{U}(boldsymbol{x})= )
( boldsymbol{k}|boldsymbol{x}|^{3}, ) where ( boldsymbol{k} ) is a positive constant. If
the amplitude of oscillation is ( a ), then
its time period ( boldsymbol{T} ) is:
A . proportional to ( frac{1}{sqrt{a}} )
B. independent of ( a )
c. proportional to ( sqrt{a} )
D. proportional to ( a^{3 / 2} )
11
433Displacement time equation of a
particle executing SHM is ( boldsymbol{x}= ) ( 10 sin left(frac{pi}{3} t+frac{pi}{6}right) c m . ) The distance
covered by particle in 3 seconds is
A. ( 5 mathrm{cm} )
B. 20 cm
c. ( 10 mathrm{cm} )
D. ( 15 mathrm{cm} )
11
434The maximum value attained by the tension in the string of a swinging pendulum is four times the minimum value it attains. There is no slack in the
string. The angular amplitude of the pendulum is?
A ( cdot 90^{circ} )
B. ( 60^{circ} )
( c cdot 45^{circ} )
D. ( 30^{circ} )
11
435The amplitude of a damped oscillator decreases to 0.9 times its original
magnitude is ( 5 s . ) In another ( 10 s ) it will
decrease to ( alpha ) times its original
magnitude, where ( alpha ) equals.
A . 0.81
B. 0.729
c. 0.6
D. 0.7
11
436Which of the following equation does
not represent a SHM?
( mathbf{A} cdot cos omega t+sin omega t )
( mathbf{B} cdot sin omega t-cos omega t )
c. ( 1-sin 2 omega t )
( mathbf{D} cdot sin omega t+cos (omega t+alpha) )
11
437If a simple pendulum has significant amplitude (up to a factor of ( 1 / ) e of original) only in the period between ( t= ) ( 0 s ) to ( t=tau s, ) then ( tau ) may be called the
average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with b’ as the constant proportionality, the average life time of the pendulum in seconds (assuming damping is small) in second :-
A. ( frac{0.693}{b} )
B. ( b )
c. ( frac{1}{b} )
D. ( frac{2}{b} )
11
438Swinging of table fan is an example of which type of motion?
A. Oscillatory motion
B. One dimenetional motion
c. Projectile motion
D. None of the above
11
439The displacement of an oscillating particle varies with time ‘t’ (in seconds) ( operatorname{according} operatorname{as} x=2 cos (0.5 pi t) ) metre
Then amplitude and time period are :
( A cdot 1 m, 4 s )
B. 2 ( m, 4 ) s
( c cdot 2 m, 2 s )
D. ( 1 mathrm{m}, 2 mathrm{s} )
11
440The displacement of a body executing SHM is given by ( x=A sin left(2 pi t+frac{pi}{3}right) . ) The first time from ( t=0 ) when the velocity is maximum is:
A. 0.33 sec
B. 0.16 sec
c. ( 0.25 mathrm{sec} )
D. ( 0.5 mathrm{sec} )
11
441In damped vibrations, as time progresses, amplitude of oscillation
A. decreases
B. increases
c. Remains same
D. Data insufficient
11
442A particle executes ( S . H . M . ) of
amplitude ( a )
1- At what distance from mean position is its kinetic energy equal to its potential energy
2- At what points is its speed half the maximum speed
11
443Displacement of a particle executing simple harmonic motion is represented by ( boldsymbol{Y}=mathbf{0 . 0 8} sin left(3 pi t+frac{pi}{4}right) ) metre.
Then calculate:-
(a) Time period.
(b) Initial phase
(c) Displacement from mean position at ( t=frac{7}{36} ) sec.
11
444Classify the following as linear, circular, vibratory or oscillatory motion.
¡) The motion of a swing.
ii) The motion of earth around the sun
iii) The motion of a cyclist on a plain
iv) The motion of a falling stone
v) The motion of a plucked string of a sitar.
11
445A particle executes SHM in a straight line. The maximum speed of the particle
during its motion is ( V_{text {max}} ). Then the average speed of the particle during the SHM is :
A ( cdot frac{V_{m}}{pi} )
в. ( frac{V_{m}}{2 pi} )
c. ( frac{2 V_{m}}{pi} )
D. ( frac{3 V_{m}}{pi} )
11
446Assertion:In simple harmonic motion A
is the amplitude of oscillation. If ( t_{1} ) be
the time to reach the particle from mean position to ( frac{A}{sqrt{2}} ) and ( t_{2} ) the time to reach from ( frac{boldsymbol{A}}{sqrt{mathbf{2}}} ) to ( mathbf{A}, ) then ( boldsymbol{t}_{mathbf{1}}=frac{boldsymbol{t}_{mathbf{2}}}{sqrt{mathbf{2}}} )
Reason : Equation of motion for the particle starting from mean position is ( operatorname{given} operatorname{by} x=A cos (omega t) ) and of the
particle starting from extreme position is given by ( boldsymbol{A} sin (boldsymbol{omega} boldsymbol{t}) )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
447The piston in the cylinder head of a locomotive has a stroke (twice the
amplitude) of ( 1.0 mathrm{m} . ) If the piston moves with simple harmonic motion with an angular frequency of 200 rad/min, what it its maximum speed?
11
448A body executes simple harmonic motion. The potential energy (P.E.), the kinetic energy(K.E.) and total energy (T.E.) are measured as function of
displacement x. Which of the following
statement is true?
A. K.E. is maximum when ( x=0 )
B. T.E. is zero when ( x=0 )
c. K.E. is maximum when x is maximum
D. P.E. is maximum when ( x=0 )
11
449Which of the following
regarding oscillatory motion is true?
A. Motion of the earth is periodic but not oscillatory because it is not to and fro.
B. Quivering of the string of the musical instrument is an example of oscillatory motion
C. Motion of the earth is periodic and oscillatory motion because it is not to and fro.
D. None of the above
11
450A particle executes S.H.M. of period
( 6.28 s ) and amplitude ( 3 mathrm{cm} . ) Its maximum acceleration is
A ( .2 .14 mathrm{cm} / mathrm{s}^{2} )
в. 3 ст / ( s^{2} )
c. ( 9.42 mathrm{cm} / mathrm{s}^{2} )
D. ( 1.5 mathrm{cm} / mathrm{s}^{2} )
11
451Which of the following results in more energy in a wave?
A. a smaller wavelength
B. a lower frequency
c. a shallower amplitude
D. a lower speed
11
452If the displacement equation of a particle from its mean position is given as ( boldsymbol{y}=mathbf{0 . 2} sin (mathbf{1 0} boldsymbol{pi} boldsymbol{t}+ )
( 1.5 pi) cos (10 pi t+1.5 pi) ) then, the
motion of particle is
A. Non-periodic
B. Periodic but not SHM
c. SHM with period 0.2
D. SHM with period 0.1 s
11
453A spring mass system oscillates with a
time period ( T_{1} ) when a certain mass is
attached to the spring. When a different mass is attached after removing the
first mass the time period becomes ( T_{2} )
When both the masses are attached to
the free end of the spring with the other end fixed, the time period of oscillation is :
( mathbf{A} cdot sqrt{T_{1} T_{2}} )
в. ( T_{1}+T_{2} )
c. ( frac{T_{1}+T_{2}}{2} )
D. ( sqrt{T_{1}^{2}+T_{2}^{2}} )
11
454In a particle executing SHM, the following parameter at equilibrium will have its
A. Kinetic energy as maximum
B. Potential energy as maximum
C. Kinetic energy as minimum
D. None of the above
11
455Consider the situation shown in figure. Show that if the blocks are displaced slightly in opposite directions and released, they will execute simple harmonic motion. Calculate the time
period.
uculate
11
456( i= )
( k )
( L )
11
457Choose the correct option which describe the simple harmonic motion.
I. The acceleration is constant.
II. The restoring force is proportional to the displacement
III. The frequency is independent of the
amplitude.
A. Il only
B. I and II only
c. I and III only
D. Il and III only
E. I, II and III
11
458In a simple harmonic motion ( (mathrm{SHM}) )
which of the following does not hold?
A. The force on the particle is maximum at the ends
B. The acceleration is minimum at the mean postion
C. The potential energy is maximum at the mean position
D. The kinetic energy is maximum at the mean position
11
459rooe vaurauestion
a, which of the following graph is
11
460In a SHM, when the displacement is one half the amplitude, what fraction of the total energy is kinetic?
A. zero
B. ( 1 / 4 )
( c cdot 1 / 2 )
D. 3/4
11
461Equation of SHM is ( x=10 sin 10 pi t . ) Then the time period is, ( x ) is in ( mathrm{cm} ) and ( mathrm{t} ) is in
( sec )
( A cdot 10 pi )
B. 0.2 sec
c. ( 0.1 mathrm{sec} )
D. 2 sec
11
462The phase difference between the two
simple harmonic oscillations, ( boldsymbol{y}_{1}= ) ( frac{1}{2} sin omega t+left(frac{sqrt{3}}{2}right) cos omega t ) and ( y_{2}= )
( sin omega t+cos omega t ) is
A ( cdot frac{pi}{6} )
B. ( -frac{pi}{6} )
c. ( frac{pi}{12} )
D. ( frac{7 pi}{12} )
11
463The torque equation for a physical
pendulum making an angle ( theta ) with the vertical is given by
A ( cdot d^{2} theta / d t^{2}=-(m g L / I) cos theta )
B . ( d^{2} theta / d t^{2}=-(m g L / I) sin theta )
C ( cdot d^{2} theta / d t^{2}=-(m g L / 2 I) sin theta )
D ( cdot d^{2} theta / d t^{2}=-(m g L / 2 I) cos theta )
11
464Why does the amplitude of a vibrating body continuously decrease during damped vibrations?11
465The periodic time of a particle doing simple harmonic motion is 4 s. The time taken for it to go from its mean position to half the maximum displacement (amplitude) is.
( mathbf{A} cdot 2 s )
B . ( 1 s )
c. ( frac{2}{3} s )
D. ( frac{1}{3} s )
11
466Which of the following statement(s)
is/are correct regarding the amplitude
vs frequency curve for a driven system? This question has multiple correct options
A. Smaller the damping, taller and narrower the resonance peak
B. The amplitude tends to infinity when it equals to natural frequency results in zero damping
C. The resonant amplitude decreases with increasing damping
D. Small damping results in driving frequency almost equal to natural frequency
11
467When a body is in SHM, match the
statements in Column A with that in
Column B
Column A
Column B
a) Velocity is maximum
e) At half of the amplitude
b) Kinetic energy is At the mean position ( 3 / 4 ) th of total energy
c) Potential energy is
g) At extreme position ( 3 / 4 ) th of total energy
d) Acceleration is
h) ( mathrm{At} sqrt{3} / 2 ) times amplitude maximum
A. a-f, b-e, c-h, d-g
B. a-e, b-f, c-g, d-h
c. a-g, b-h, c-e, d-f
D. a-h, b-e, c-f, d-e
11
468A leapord leaps a distance of 1 metre in a straight line, 20 times in 1 minute, while catching a prey, then
A. Time period and frequency cannot be determined since the leopard is not returning to its original position
B. The product of its time period and frequency will be unity
c. The time period is infinity
D. The frequency is zero
11
469How many times will light travel around
the Earth in one second?
A. 7 times
B. 5 times
c. 3 times
D. 9 times
11
470Which of the following quantities are always zero in SHM? This question has multiple correct options
A ( cdot vec{F} times vec{a} )
В. ( vec{v} times vec{r} )
c ( . vec{a} times vec{r} )
D. ( vec{F} times vec{r} )
11
471Two particles ( P ) and ( Q ) describe simple harmonic motions of same period,
same amplitude, along thesame line about the same equilibrium position 0 When ( P ) and ( Q ) are on opposite sides of 0 at the samedistance from 0 they have the same speed of ( 1.2 mathrm{m} / mathrm{s} ) in the same direction, when their displacements arethe same they have the same speed of ( 1.6 mathrm{m} / mathrm{s} ) in opposite directions. The maximum velocity in ( mathrm{m} / mathrm{s} ) ofeither
particle is
A . 2.8
B. 2.5
( c cdot 2.4 )
D. 2
11
472one end has a small block of mass ( m )
and charge ( q ) is attached at the other
end. The block rests over a smooth
horizontal surface. A uniform and
constant magnetic field ( B ) exists
normal to that plane of paper as shown in figure. An electric field ( overrightarrow{boldsymbol{E}}=boldsymbol{E}_{0} hat{boldsymbol{i}}left(boldsymbol{E}_{mathbf{0}}right. )
is a positive constant) is switched on at
( boldsymbol{t}=mathbf{0} ) sec. The block moves on horizontal
surface without ever lifting off the
surface. Then the normal reaction
acting on the block is
A. Maximum at extreme position and minimum at mean position
B. Maximum at mean position and minimum at extreme position
C. is uniform throughout the motion
D. is both maximum and minimum at mean position
11
473A Simple harmonic oscillator has a period of ( 0.01 s ) and an amplitude of ( 0.2 m . ) The magnitude of the velocity in ( m ) ( sec ^{-1} ) at the mean position will be
A ( .20 pi )
в. 100
c. ( 40 pi )
D. ( 100 pi )
11
474Variations of acceleration a of a particle executing SHM with displacement x is:11
475The energy of a particle executing simple harmonic motion is given by the equation ( boldsymbol{E}=boldsymbol{A} boldsymbol{x}^{2}+boldsymbol{B} boldsymbol{v}^{2} ) where ( boldsymbol{x} ) is the
displacement from mean position ( boldsymbol{x}= )
0 and ( v ) is the velocity of the particle at
( x . ) Find the amplitude of ( S . H . M )
11
476Which of the following is not simple
harmonic function?
A ( cdot y=a sin 2 omega t+b cos ^{2} omega t )
B. ( y=a sin omega t+b cos 2 omega t )
c. ( y=1-2 sin ^{2} omega t )
D ( cdot y=(sqrt{a^{2}+b^{2}}) sin omega t cos omega t )
11
477A particle performing SHM has time period ( frac{2 pi}{sqrt{3}} ) and path length ( 4 mathrm{cm} . ) The
displacement from mean position at which acceleration is equal to velocity is
( A cdot 0 c m )
B. ( 0.5 mathrm{cm} )
( c cdot 1 c m )
D. ( 1.5 mathrm{cm} )
11
478An object of mass ( 0.2 mathrm{kg} ) executes SHM along the ( x ) -axis with frequency
( (25 / pi) H z . A t ) the point ( x=0.04 m ) the
object has ( mathrm{KE} 0.5 mathrm{J} ) and PE 0.4 J.The amplitude of oscillation (in cm) is
11
479If
( x, v ) and ( a ) denote the displacement the velocity and the acceleration of a particle executing simple harmonic
motion of time period ( T, ) then, which of
the following does not change with time?
в. ( frac{mathrm{aT}}{mathrm{x}} )
c. ( a T+2 pi v )
D. ( frac{mathrm{aT}}{mathrm{v}} )
11
480For a particle in SHM, if the amplitude of the displacement is ( alpha ) and the
amplitude of velocity is ( v, ) the amplitude of acceleration is
A ( . v alpha )
в. ( frac{v^{2}}{alpha} )
c. ( frac{v^{2}}{2 alpha} )
D. ( underline{v} )
11
481The kinetic energy of a simple
pendulum may be decreased by:
A. increasing the mass of the bob
B. increasing the thickness of the string
C. decreasing the length of the string
D. increasing the length of the string
E. decreasing the displacement of the string
11
482The frequency ( f ) of vibration of mass ( m )
suspended from a spring of spring
contact ( k ) is given by ( boldsymbol{f}=boldsymbol{c} boldsymbol{m}^{boldsymbol{x}} boldsymbol{k}^{boldsymbol{y}} )
Where ( c= ) dimensionless constant
then find the values of ( x ) and ( y )
11
483The work done in stretching a spring of force constant ( mathrm{k} ) from ( boldsymbol{y}_{1} ) and ( boldsymbol{y}_{2} ) from
mean position will be
A ( cdot frac{k}{2}left(y_{2}^{2}-y_{1}^{2}right) )
B. ( frac{k}{2}left(y_{1}^{2}-y_{2}^{2}right) )
( mathbf{c} cdot kleft(y_{2}-y_{1}right) )
D. zero
11
484The correct relation between frequency and time period is
( ^{mathbf{A}} cdot T=frac{1}{f} )
B ( cdot T=sqrt{frac{1}{f}} )
c. ( T=frac{1}{2 f} )
D. ( T=frac{2}{f} )
11
485Two simple Harmonic Motions of
angular frequency 100 and 1000 rad ( S^{-1} )
have the same displacement amplitude. The ratio of their maximum accelerations is :
A ( cdot 1: 10^{3} )
B ( cdot 1: 10^{4} )
c. 1: 10
D. ( 1: 10^{2} )
11
486( frac{1}{0} )
( frac{partial}{t} )
11
487If the displacement, velocity and acceleration of particle in ( S H M ) are
( mathbf{1} boldsymbol{c m}, mathbf{1} boldsymbol{c m} / boldsymbol{s e c} ) and ( mathbf{1} boldsymbol{c m} / boldsymbol{s e c}^{mathbf{2}} )
respectively its time period (in secs) will be:
A . ( pi )
B. ( 0.5 pi )
( c .2 pi )
D. ( 1.5 pi )
11
488A particle of ass ( mathrm{m} ) and charge ( mathrm{Q} ) is placed in an electric field E which varies
with time ( t ) ass ( E=E_{0} ) sin ( omega t . ) It will undergo simple harmonic motion of amplitude
A ( cdot frac{Q E_{0}^{2}}{m omega^{2}} )
в. ( frac{Q E_{0}}{m omega^{2}} )
c. ( sqrt{frac{Q E_{0}}{m omega_{2}}} )
D. ( frac{Q E_{0}}{m omega} )
11
489The potential energy of a simple harmonic oscillator of mass ( 2 mathrm{kg} ) in its mean position is 5 J. If its totalenergy is
( 9 mathrm{J} ) and its amplitude is ( 0.01 mathrm{m}, ) its time period would be
A. ( pi / 10 ) sec
B . ( pi / 20 mathrm{sec} )
c. ( pi / 50 ) sec
D. ( pi / 100 ) sec
11
490Match the items in List 1 with the items
in List 2
11
491A student says that he had applied a force ( F=-k sqrt{x} ) on a particle and the
particle moves in simple harmonic
motion. He refuses to tell whether ( k ) is a
constant or not. Assume that he has
worked only with positive ( x ) and no other
force acted on the particle.
A . As ( x ) increases ( k ) increases
B. As ( x ) increases ( k ) decreases
C. As ( x ) increases ( k ) remains constant
D. The motion cannot be simple harmonic
11
492Earth revolves around sun in 365
days.Calculate its angular speed.
11
493A rope, under a tension of ( 200 N ) and
fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by ( : boldsymbol{y}=mathbf{0 . 1} sin left(frac{boldsymbol{pi} boldsymbol{x}}{mathbf{2}}right) sin 12 boldsymbol{pi} boldsymbol{t} )
Where ( x=0 ) at one end of the rope, ( x ) is
in meters and ( t ) is in seconds. The speed of the progressive waves ( (operatorname{in} m / s) ) on the rope is
11
494Two particles execute SHM of same amplitude and same time period, about
same mean position but with a phase difference between them. At an instant
they are found to cross each other at
( x=+frac{A}{3} . ) The phase difference between
them is:
( mathbf{A} cdot 2 cos ^{-1}left[frac{1}{5}right] )
B ( cdot 2 sin ^{-1}left[frac{1}{5}right] )
C ( cdot 2 cos ^{-1}left[frac{1}{3}right] )
D. ( 2 sin ^{-1}left[frac{1}{3}right] )
11
495The particle is executing S.H.M. on a line ( 4 mathrm{cms} ) long. If its velocity at its mean position is ( 12 mathrm{cm} / mathrm{sec}, ) its frequency in Hertz will be :
A ( cdot frac{2 pi}{3} )
в. ( frac{3}{2 pi} )
c.
D. ( frac{3}{pi} )
11
496A simple harmonic oscillator has a period ( T ) and energy E. The amplitude of the oscillator is doubles. Choose the
A. Period and energy get doubled
B. Period gets doubled while energy remains the same.
c. Energy gets doubled while period remains the same
D. Period remains the same and energy becomes four times
11
497The period of the SHM of a particle with
the maximum velocity ( 50 mathrm{cm} / mathrm{s} ) and maximum acceleration ( 10 mathrm{cm} / mathrm{s}^{2} ) is
A . ( 31.42 s )
B. ( 6.284 s )
c. ( 3.142 s )
D. ( 0.3124 s )
11
498Calculate the velocity of the bob of a
simple pendulum at its mean position if it is able to rise to a vertical height of ( 10 mathrm{cm} . ) Given: ( g=980 mathrm{cms}^{-2} )
11
499A particle executes simple harmonic motion along a straight line with mean position at ( x=0 ) and period of ( 20 s ) and amplitude of ( 5 mathrm{cm} . ) The shortest time taken by the particle to go from ( boldsymbol{x}=mathbf{4 c m} ) to ( boldsymbol{x}=-mathbf{3 c m} ) is
A . ( 4 s )
B. 7 s
( c .5 s )
D. ( 6 s )
11
500Statement 1: In simple harmonic motion, the motion is to and fro and
periodic.

Statement 2: Velocity of the particle
( (v)=omega sqrt{k^{2}-x^{2}} ) (where ( x ) is the
displacement).
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 is the correct explanation for Statement 1
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false

11
501The simple harmonic motion of a particle is given by ( boldsymbol{x}=boldsymbol{a} sin 2 boldsymbol{pi} boldsymbol{t} . ) Then
the location of the particle from its
mean position at a time ( 1 / 8 ) th of a second is:
( mathbf{A} cdot boldsymbol{a} )
B. ( frac{a}{2} )
c. ( frac{a}{sqrt{2}} )
D. ( frac{a}{4} )
E ( cdot frac{a}{8} )
11
502A tunnel is dug along the diameter of the earth. A mass ( m ) is dropped into it. How much time does it take to cross the
earth?
A. 169.2 minutes
B. 84.6 minutes
c. 21.2 minutes
D. 42.3 minutes
11
503If the displacement of a particle executing SHM is given by ( boldsymbol{y}= )
( 0.30 sin (220 t+0.64) ) in metre, then the
frequency and maximum velocity of the particle are
A ( .35 H z, 66 m / s )
B. ( 45 H z, 66 m / s )
( mathbf{c} .58 H z, 113 m / s )
D. ( 35 H z, 132 m / s )
11
504Two particles are in SHM along same line. Time period of each is ( T ) and
amplitude is ( A . ) After how much time
will they collide if at time ( t=0 . ) First particle is at ( x_{1}=+frac{A}{2} ) and moving
towards positive ( x- ) axis and second particle is at ( x_{2}=-frac{A}{sqrt{2}} ) and moving
towards negative ( x- ) axis.
A ( cdot frac{18}{19} T )
в. ( frac{19}{48} mathrm{T} )
c. ( frac{48}{19} T )
D. ( frac{19}{18} mathrm{T} )
11
505Restoring force in the SHM is
A. conservative
B. nonconservative
C . frictional
D. centripetal
11
506The displacement of a particle is
represented by the equation ( y= ) ( 3 cos left[frac{pi}{4}-2 omega tright] )
The motion is:
A. non- periodic
B. periodic but not simple harmonic
c. simple harmonic with period 2 piw
D. simple harmonic with period ( left(frac{pi}{omega}right) )
11
507In a Vander waals interaction: ( boldsymbol{U}= )
( boldsymbol{U}_{0}left[left(frac{boldsymbol{R}_{0}}{boldsymbol{r}}right)^{12}-boldsymbol{2}left(frac{boldsymbol{R}_{0}}{boldsymbol{r}}right)^{6}right] )
A small displacement x is given from
equilibrium position ( r=R_{0} . ) Find the
approximate PE function.
A ( cdot frac{36 U_{0}}{R_{0}^{2}} x^{2}-U_{0} )
в. ( frac{24 U_{0}}{R_{0}} x-U_{0} )
c. ( frac{96 U_{0}}{R_{0}^{2}}-U_{0} )
D. none of these
11
508A particle executes SHM on a straight line path. The amplitude of oscillation is ( 2 mathrm{cm} . ) When the displacement of the
particle from the mean position is ( 1 mathrm{cm} ) the numerical value of the magnitude of
acceleration is equal to the numerical
value of the magnitude of the velocity.
The frequency of SHM is:
( A cdot 2 pi sqrt{3} )
B. ( frac{2 pi}{sqrt{3}} )
( c cdot frac{sqrt{3}}{2 pi} )
D. ( frac{1}{2 pi sqrt{3}} )
11
509In forced vibration ( boldsymbol{m}=mathbf{1 0 g m}, boldsymbol{f}= )
( 100 H z ) and driver force ( F= )
( 100 cos (20 pi t) ) then what amplitude of
particle.
11
510A mass ( m, ) which is attached to a
spring with constant ( k, ) oscillates on a
horizontal table, with amplitude ( A . ) At
an instant when the spring is stretched by ( sqrt{3} A / 2, ) a second mass ( m ) is dropped
vertically onto the original mass and immediately sticks to it. What is the amplitude of the resulting motion?
A ( cdot frac{sqrt{3}}{2} A )
B. ( sqrt{frac{7}{8}} A )
c. ( sqrt{frac{13}{16}} A )
D. ( sqrt{frac{2}{3}} A )
11
511If a simple pendulum of length L has maximum angular displacement ( boldsymbol{theta} ) then the maximum kinetic energy of the
bob of mass ( mathrm{m} ) is
A ( cdot frac{1}{2} m(L / g) )
В. ( m g L(1-cos theta) )
c. ( (m g L sin theta) / 2 )
D. ( m g / 2 L )
11
512Three similar oscillators, ( A, B, C ) have the same small damping constant ( r )
but different natural frequencies ( omega_{0}= ) ( (k / m)^{frac{1}{2}}: 1200 H z, 1800 H z, 2400 H z .1 f )
all three are driven by the same source at ( 1800 H z, ) which statement is correct
for the phases of the velocities of the
three?
A ( cdot phi_{A}=phi_{B}=phi_{c} )
в. ( phi_{A}<phi_{B}=0phi_{B}=0>phi_{c} )
D ( cdot phi_{A}>phi_{B}>0>phi_{c} )
11
513A weakly damped harmonic oscillator is executing resonant oscillations. The phase difference between the oscillator
and the external periodic force is:
A. zero
B . ( pi / 4 )
c. ( pi / 2 )
( D )
11
514Which of the following quantity does not change due to damping of oscillations?
A. Angular frequency
B. Time period
c. Initial phase
D. Amplitude
11
515Choose the correct statement with
respect to the graph given(consider the
case of simple mass spring, ( ) )
A. A force must be acting on the system
B. B represent kinetic energy
C. A represent potential energy
D. none of the above
11
516A light spiral spring supports a 200 g weight at its lower end. It oscillates up and down with a period of 1 sec. How much weight (gram) must be removed from the lower end to reduce the period
to 0.5 sec.?
A . 200
B. 50
( c .53 )
D. 100
11
517The damping force on a oscillator is directly proportional to the velocity. The Unit of the constant of proportionality
are:
A. ( mathrm{kgs}^{-1} )
B. kgs
c. ( operatorname{kgms}^{-2} )
D. kgms
11
518The equation of a wave is given by ( boldsymbol{Y}= )
( A sin omegaleft(frac{x}{v}-kright), ) where ( omega ) is the angular
velocity and ( v ) is the linear velocity. Find
the dimension of ( k ? )
11
519The shortest distance travelled by a
particle performing SHM from its mean position in ( operatorname{secs} text { is } 1 / sqrt{(} 2) ) of its amplitude. Find its time period:
( A cdot 8 )
B. 16
( c cdot 4 )
D.
11
520Vibrations, whose amplitudes of oscillation decrease with time, are
called:
A. free vibrations
B. forced vibrations
c. damped vibrations
D. sweet vibrations
11
521If a body moves back and forth
repeatedly about a mean position, it is said to possess
A. rotatory motion
B. projectile motion
c. oscillatory motion
D. Reciprocating motion
11
522A particle of mass is executing oscillations about the origin on the ( x ) axis. Its potential energy is ( V(x)= )
( k|x|^{3}, ) where ( k ) is a positive constant. If
the amplitude of oscillation is ( a ), then
its time period ( T ) is proportional
A . proportional to ( frac{1}{sqrt{a}} )
B. proportional to ( sqrt{a} )
C . Independent ( a^{frac{3}{2}} )
D. None of these
11
523A particle in linear SHM performs ( 30 s c / s e c . ) Its velocity is ( 0.120 m / s ) when it passes through the middle of its path. The length of path is
A. ( 0.012 mathrm{cm} )
B. ( 3.2 mathrm{cm} )
c. ( 0.04 c m )
D. ( 1.2 mathrm{cm} )
11
524The equation of motion of a particle executing SHM is ( left(frac{d^{2} x}{d t^{2}}right)+k x=0 . ) The time period of the particle will be ?
A ( cdot frac{2 pi}{sqrt{k} pi} )
в. ( 2 pi )
( c cdot 2 pi k )
D. ( 2 pi sqrt{k} )
11
525The ratio of ( x_{1} / x_{2} ) is
( A cdot 2 )
B. ( frac{1}{2} )
( c cdot sqrt{2} )
D. ( frac{1}{sqrt{2}} )
11
526The vibrations of a body which take place under the influence of an external
periodic force acting on it are called
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All
11
527A silver atom in a solid oscillates in
simple harmonic motion in some
direction with a frequency of ( 10^{12} / ) sec.
What is the force constant of the bonds
connecting one atom with the other? (Mole wt. of silver ( =108 ) and Avagadro
number ( =mathbf{6 . 0 2} times mathbf{1 0}^{mathbf{2 3}} mathbf{g} mathbf{m} mathbf{m o l}^{-mathbf{1}} ) ).
A. ( 2.2 mathrm{N} / mathrm{m} )
в. ( 5.5 mathrm{N} / mathrm{m} )
c. ( 6.4 mathrm{N} . mathrm{m} )
D. ( 7.1 mathrm{N} / mathrm{m} )
11
528A particle executing SHM is described
by the equation ( boldsymbol{x}=boldsymbol{A} boldsymbol{e}^{boldsymbol{omega} t} ). Will this
particle describe SHM.
A. It dosen’t execute SHM
B. It executes SHM only for the first time
c. It executes SHM from ( x=0 ) to ( x=A )
D. It executes SHM from ( x=0 ) to ( x=-A )
11
529A particle of mass ( 2 mathrm{kg} ) is moving on a straight line under the action of force ( mathrm{F}= ) ( (8-2 x) ) newton along the ( x ) -axis where ( x ) is the coordinates on ( x ) -axis If a particle
is released from ( x=7 ) m then for the
subsequent motion match the following (all values in Column II are in S.I units)
11
530For the given experimental setup, the oscillation frequency of the mass is
( boldsymbol{f} cdot boldsymbol{S}_{1} ) and ( boldsymbol{S}_{2} ) are identical springs. One
spring is now removed, then frequency
will become.
A . ( 2 f )
B. ( frac{f}{sqrt{2}} )
c. ( frac{f}{sqrt{3}} )
D. ( sqrt{2} f )
11
531A spring mass system is in simple harmonic motion. Immediately after the upward extreme end point, which of the following increase?
A. Kinetic energy, gravitational potential energy, elastic potential energy
B. Kinetic energy and gravitational potential energy
c. Kinetic energy only
D. Gravitational potential energy and elastic potential energy
E. Elastic potential energy only
11
532A mass at the end of a spring executes harmonic motion about an equilibrium position with an amplitude A.lts speed as it passes through the equilibrium position is V.If extended 2A and released, the speed of the mass passing through the equilibrium position will be
A ( .2 v )
B. 4V
c. v/2
D. V/4
11
533Which of the following motions is not simple harmonic?
A. Vertical oscillations of a spring
B. Motion of a simple pendulum
c. Motion of planet around the sun
D. oscillation of liquid in a U-tube
11
534Find the natural frequency of oscillation
of the system as shown in figure. Pulleys are massless and frictionless.
Spring and string are also massless.
A ( cdot frac{pi}{2} )
B. ( sqrt{pi} )
( c cdot sqrt{frac{1}{pi}} )
( D )
11
535Obtain an expression for potential energy of a particle performing simple harmonic motion. Hence evaluate the
potential energy (a) at mean position and (b) at extreme position. A horizontal
disc is freely rotating about a transverse axis passing through its centre at the rate of 100 revolutions per
minute. A 20 gram blob of wax falls on
the disc and sticks to the disc at a
distance of ( 5 mathrm{cm} ) from its axis. Moment
of inertia of the disc about its axis
passing through its centre of mass is ( 2 times 10^{-4} k g m^{2} . ) Calculate the new
frequency of rotation of the disc.
11
536A block is attached to an unstretched vertical
spring and released from rest. As a result of
This the block comes down due to its weight.
stops momentarily, and then bounces back.
Finally, the block starts oscillating up and
down.
M
Fig. 6.389
During oscillations, match Column I with Column II:
Column I
Column II
When the block is at its a. Acceleration is in
maximum downward upward direction.
displacement position (may
be known as extreme
position)
When the block is at its b. Acceleration is in
equilibrium position
downward direction.
When the block is somewhere c. Acceleration is zero.
between equilibrium position
and downward extreme
position
When the block is above d. Velocity may be
equilibrium position but in upward or in
below the initial unstretched downward direction.
position
.
!
iv.
11
537The time period of a particle in SHM is
12 sec. At ( t=0, ) it is at mean position. The ratio of the distance travelled in the
second and sixth second is.
A ( cdot(sqrt{3-1}) )
B. ( (sqrt{2-1}) )
c. ( frac{1}{(sqrt{2}-1)} )
D. ( frac{1}{sqrt{2}} )
11
538The periodic vibrations of a body of decreasing amplitude in the presence of resistive force on it are called
A. Forced vibrations
B. Free vibration
c. Damped vibrations
D. All
11
539toppr ०६
spring is unsurtecritu. Next with the blue mass hanging, the
spring stretches.

Finally, with the red mass hanging, the
spring stretches twice as much as it
did with blue mass.
How much energy does the hanging red
mass store in the spring-mass system,
compared to the amount of energy the
hanging blue mass stores in the spring-
mass system?
A. The red mass stores twice as much energy as the blue mass
B. The red mass stores fours times as much energy as the blue mass
C. The red mass stores half as much energy as the blue mass
D. The red mass stores about 1.4 times as much energy as the blue mass
E. We cannot determined how much energy the red mass stores compared to the blue mass, because we do not know the unstretched length of the spring

11
540A particle doing S.H.M. having
amplitude ( 5 mathrm{cm}, ) mass ( 5 mathrm{kg} ) and angular
frequency 5 is 1 cm from mean position.
Find potential energy and kinetic
energy.
( mathbf{A} cdot K cdot E .=150 times 10^{-4} J . P . E .=6.25 times 10^{-4} J )
B . ( K . E .=6.25 times 10^{-4} J . P . E .=150 times 10^{-3} J )
C ( . K . E .=6.25 times 10^{-4} J . P . E .=6.25 times 10^{-4} J )
D . ( K . E .=150 times 10^{-3} mathrm{J.P.E.}=150 times 10^{-4} mathrm{J} )
11
541What is the number of degrees of
freedom of an oscillating simple pendulum?
A. more than three
B. 3
( c cdot 2 )
D.
11
542A particle is acted simultaneously by mutually perpendicular simple harmonic motions ( x=a c o s omega t ) and ( y= )
asinwt. The trajectory of motion of the
particle will be
A. an ellipse
B. a parabola
c. a circle
D. a straight line
11
543Assertion
Motion of a ball bouncing elastically in
vertical direction on a smooth
horizontal floor is a periodic motion, but
not an SHM.
Reason
Motion is SHM when restoring force is proportional to displacement from
mean position.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
544An ant moves along a circle 5 times in 1
minute with a uniform speed and a
lizard moves in a straight line to and fro
5 times in 5 minutes. Then
A. The motion of the ant is uniformly accelerated but non periodic
B. The motion of the lizard is uniformly accelerated but non periodic
C. Both ant and lizard are periodic
D. Both ant and lizard are accelerated and their direction
is along the direction of velocity
11
545The displacement of a particle varies
with time according to the relation ( y= )
asinomegat ( + )bcosomegat.
A. The motion is oscillatory but not SHM.
B. The motion is SHM with amplitude a + b.
c. The motion is SHM with amplitude ( a^{2}+b^{2} )
D. The motion is SHM with amplitude ( sqrt{a^{2}+b^{2}} )
11
546A force acts on a ( 30 mathrm{gm} ) particle in such a way that the position of the particle as a function of time is given by ( boldsymbol{x}=mathbf{3} boldsymbol{t}- )
( 4 t^{2}+t^{3}, ) where ( x ) is in metres and ( t ) is in
seconds. The work done during the first
4 second is?
A .5 .28
B. 450mJ
c. ( 490 mathrm{mJ} )
D. 530 mJ
11
547A particle undergoes SHM with a time period of 2 seconds. In how much time will it travel from its mean position to a displacement equal to half of its
amplitude?
A ( cdot(1 / 2) s )
в. ( (1 / 3) s )
c. ( (1 / 4) s )
D. ( (1 / 6) s )
11
548Instantaneous displacement of a particle is ( y=4 cos ^{2}left(frac{t}{2}right) sin 1000 t )
The particle is displaced due to:
A. only one wave
B. two waves
c. three waves
D. four waves
11
549Displacement time equation of a
particle SHM is ( boldsymbol{x}= ) ( mathbf{1 0} sin left(frac{boldsymbol{pi}}{mathbf{3}} boldsymbol{t}+frac{boldsymbol{pi}}{mathbf{6}}right) boldsymbol{c m} . ) The distance
covered by particle in ( 3 s ) is
A . ( 5 mathrm{cm} )
B. ( 20 mathrm{cm} )
c. ( 10 mathrm{cm} )
D. ( 15 mathrm{cm} )
11
550A stone is swinging in a horizontal circle of diameter ( 0.8 ~ m ) at 30 rev / min. A distant light causes a shadow of the stone on a nearly wall. The amplitude and period of the SHM for the shadow of the stone are:
A. ( 0.4 m, 4 s )
B. ( 0.2 m, 2 s )
c. ( 0.4 m, 2 s )
D. ( 0.8 m, 2 s )
11
551A particle of mass ( 0.5 mathrm{kg} ) is executing SHM along a straight line. Its path length is ( 10 mathrm{cm} ) and time period is 8s. TE
when its phase angle is ( frac{pi}{6} ) radian is
B. 0.964×10-4 J
c. ( 3.856 times 10^{-4} ) j
D. 4.324×10-4 J
11
552The equation of motion for an oscillating particle is given by
( boldsymbol{x}=boldsymbol{3} sin (boldsymbol{4} boldsymbol{pi} boldsymbol{t})+boldsymbol{4} cos (boldsymbol{4} boldsymbol{pi} boldsymbol{t}), ) where ( boldsymbol{x} ) is
in mm and t is in second
This question has multiple correct options
A. The motion is simple harmonic
B. The period of oscillation is 0.5 s
c. The amplitude of oscillation is ( 5 mathrm{mm} )
D. The particle starts its motion from the equilibrium
11
553n figure, ( boldsymbol{k}=mathbf{1 0 0} boldsymbol{N} / boldsymbol{m}, boldsymbol{M}= )
1 kgand ( F=10 N . ) Write the potential
energy of the spring when the block is at the right extreme during simple harmonic motion
If your answer is ( x ) write the value of ( 4 x )
11
554Two strings ( A ) and ( B ) have lengths ( i_{A} )
and ( l_{B} ) and carry pendulum of masses
( M_{A} ) and ( M_{B} ) at their lower ends the
upper ends being supported by rigid
supports. If ( n_{A} ) and ( n_{B} ) are their
frequencies of their oscillations and
( boldsymbol{n}_{boldsymbol{A}}=boldsymbol{2} boldsymbol{n}_{boldsymbol{B}}, ) then :
A ( . l_{A}=4 l_{B} ), regardless of masses
B . ( l_{B}=4 l_{4}, ) regardless of masses
C . ( M_{A}=2 M_{B}, l_{A}=2 l_{B} )
D. ( M_{B}=2 M_{A}, l_{B}=2 l_{A} )
11
555The displacement of a particle along the
( x ) -axis is given by ( x=a sin ^{2} t . ) The motion
of the particle corresponds to
A. simple harmonic motion of frequency ( omega / pi )
B. simple harmonic motion of frequency 3 ( omega / 2 pi )
c. non simple harmonic motion
D. simple harmonic motion of frequency ( omega / 2 pi )
11
556A uniform thin ring of radius ( boldsymbol{R} ) and
mass ( m ) suspended in a vertical plane from a point in its circumference its time period of oscillation is
A ( cdot 2 pi sqrt{frac{2 R}{g}} )
В ( cdot 2 pi sqrt{frac{3 R}{2 g}} )
c. ( frac{pi}{2} sqrt{frac{R}{g}} )
D. ( pi sqrt{frac{R}{2 g}} )
11
557Derive an expression for the velocity of a particle performing linear SHM using differential equation. Hence, find the expression for the maximum velocity.11
558The displacement of a particle performing linear S.H.M is given by ( boldsymbol{x}= ) ( 6 sin (3 pi t-5 pi / 6) ) metre. Find the time
at which the particle reaches the extreme position towards the left:
A. ( 5 / 9 ) secs
B . 4/9 secs
c. ( 1 / 9 ) secs
D. 7/9 secs
11
559Column I describe some situations in
which a small object moves. Column I
describes some characteristics of these
motions. Match the situation in Column
with the characteristics in Column I
and indicate your answer by darkening appropriate bubbles in the 44 matrix given in the ORS
11
560For a particle executing simple
harmonic motion, the displacement x is given by ( boldsymbol{x}= ) Acoswt. Identify the graph
which represents the variation of
potential energy (U) as a function of
time ( t ) and displacement ( x )
A . ।, II
B. ॥, ॥॥
( c cdot 1,1 v )
D. II, IV
11
561A particle of mass ( m ) is executing S.H.M If amplitude is a and frequency ( n ), the value of its force constant will be:
( mathbf{A} cdot m n^{2} )
B. ( 4 m n^{2} a^{2} )
( mathrm{c} cdot m a^{2} )
D. ( 4 pi^{2} m n^{2} )
11
562The ratio of the maximum velocity and maximum displacement of a particle executing SHM is equal to
( A cdot n )
B. ( g )
c.
( D . )
11
563Assertion
A particle is under SHM along the ( x ) axis. Its mean position is ( x=2 ) amplitude is ( A=2 ) and angular frequency
( omega . A t t=0, ) particle is at origin, then ( x-c 0 )
ordinate versus time equation of the
particle will be ( x=-2 cos omega t+2 )
Reason
At ( t=0 ) particle is at rest.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
564A function of time given by
( (sin omega t-cos omega t) ) represents
A. simple harmonic motion
B. non-periodic motion
c. periodic but not simple harmonic motion
D. oscillatory but not simple harmonic motion
11
565A student says that he had applied a force ( F=k sqrt{x} ) on a particle moved in simple harmonic motion. He refuses to
tell whether ( k ) is a constant or not.
Assume that he has worked only with
positive ( x ) and no other force acted on
the particle.
A . As ( x ) increases ( k ) increases
B. AS ( x ) increases ( k ) decreases
C. As ( x ) increases ( k ) remains constant
D. The motion cannot be simple harmonic.
11
566The differential equation of a wave is :
A ( cdot frac{d^{2} y}{d t^{2}}=v^{2} frac{d^{2} y}{d x^{2}} )
B. ( frac{d^{2} y}{d x^{2}}=v^{2} frac{d^{2} y}{d t^{2}} )
c. ( frac{d^{2} y}{d x^{2}}=frac{1}{v} frac{d^{2} y}{d t^{2} y} )
D. ( frac{d^{2} y}{d x^{2}}=-v frac{d^{2} y}{d t^{2}} )
11
567The graph between velocity and position
for a damped oscillation will be?
A. Straight line
B. Circle
C . Ellipse
D. Spiral
11
568Which of the following figure represents damped harmonic motion11
569A body is executing ( mathrm{SHM} ), At a displacement ( x, ) its potential energy is
( E_{1} ) and at a displacement ( y, ) its
potential energy is ( E_{2} ). Find its potential energy ( mathrm{E} ) at displacement ( (mathrm{x}+mathrm{y}) )
B . ( sqrt{E}=sqrt{E}_{1}+sqrt{E}_{2} )
c. none of these
D. all of these
11
570The ratio of maximum acceleration to
maximum velocity in a simple
harmonic motion ( 10 S^{-1} . A t, t=0 ) the
displacement is ( 5 mathrm{m} ). What is the maximum acceleration? The initial
phase is ( frac{pi}{4} )
( mathbf{A} cdot 750 sqrt{2} m / s^{2} )
B . ( 500 sqrt{2} mathrm{m} / mathrm{s}^{2} )
c. ( 750 m / s^{2} )
D. ( 500 m / s^{2} )
11
571A particle is performing linear S.H.M. with period 6 s and amplitude ‘a’. The minimum time taken by the particle to travel between two points situated at a distance ( frac{a}{2} ) on either sides of mean
position is :
A . 1 s
в. 1.5 s
( c cdot 3 s )
D. 6 s
11
572Statement 1: If the amplitude of a
simple harmonic oscillator is doubled,
its total energy becomes four times.
Statement 2: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic
oscillator.
A. Statement 1 is false, Statement 2 is true
B. Statement 1 is true, Statement 2 is true; Statement 2 the correct explanation for Statement
c. statement 1 is true, Statement 2 is true; Statement 2 is not the correct explanation for Statement
D. Statement 1 is true, Statement 2 is false
11
573If a system is displaced from its equilibrium position and released, it
moves according to the equation ( ddot{boldsymbol{theta}}=-frac{boldsymbol{I}^{2}}{boldsymbol{k} boldsymbol{l}} boldsymbol{theta} )
where ( I, ) k and I are constants. It will
oscillate with a frequency:
( ^{A} cdot sqrt{frac{I^{2}}{k l}} )
в. ( 2 pi sqrt{frac{k l}{I^{2}}} )
( ^{mathrm{c}} cdot frac{1}{2 pi} sqrt{frac{I^{2}}{k l}} )
D. ( frac{1}{2 pi} sqrt{frac{k l}{I^{2}}} )
11
574The maximum velocity and the maximum acceleration of a body moving in a simple harmonic oscillator
are ( 2 m / s ) and ( 4 m / s^{2} . ) The angular velocity will be:
A. ( 3 r a d / s )
B. ( 0.5 r a d / s )
c. ( 1 r a d / s )
D. ( 2 r a d / s )
11
575A particle executes simple harmonic oscillation with an amplitude ( a ). The period of oscillation is T. The minimum time taken by the particle to travel half of the amplitude from the equilibrium position is
A ( cdot frac{T}{4} )
в. ( frac{T}{8} )
c. ( frac{T}{12} )
D. ( frac{T}{2} )
11
576For periodic motion of small amplitude
( A, ) the time period ( T ) of this particle is
proportional to
( mathbf{A} cdot A sqrt{frac{m}{alpha}} )
B. ( frac{1}{A} sqrt{frac{m}{alpha}} )
c. ( A sqrt{frac{alpha}{m}} )
D. ( A sqrt{frac{2 alpha}{m}} )
11
577Select the appropriate statement from
the below:
A. The magnitude of maximum acceleration is ( A omega )
B. The magnitude of maximum acceleration is ( A omega^{2} )
c. The magnitude of minimum acceleration is ( A omega )
D. The magnitude of minimum acceleration is ( A omega / 2 )
11
578Ratio of kinetic energy at mean position to potential energy at ( A / 2 ) of a particle performing SHM.
A . 2: 1
B . 4: 1
c. 8: 1
D. 1: 1
11
579If the time period of revolution of earth is 365 days, then, the frequency of revolution of earth is
A ( cdot 3.17 times 10^{-6} mathrm{Hz} )
В. ( 3.17 times 10^{-8} mathrm{Hz} )
c. ( 3.17 times 10^{-4} mathrm{Hz} )
D. ( 3.17 times 10^{-7} mathrm{Hz} )
11
580The differential equation of a particle executing SHM along y-axis is
A ( cdot frac{d^{2} y}{d t^{2}}+omega^{2} y=0 )
B. ( frac{d^{2} y}{d t^{2}}-omega^{2} y=0 )
( ^{text {C } cdot frac{d^{2} x}{d t^{2}}+omega^{2} x=0} )
D. ( frac{d^{2} x}{d t^{2}}-omega^{2} x=0 )
11
581An oscillator is producing FM waves of frequency ( 2 mathrm{kHz} ) with avariation of
10kHz. The modulating index=?
A . 0.20
B. 5.0
c. 0.67
D. 1.5
11
582State whether true or false:
The particle is moving simple harmonically
A. True
B. False
11
583Show that motion of bob of pendulum
with small amplitude is linear ( S . H . M ) Hence obtained an expression for its period. What are the factors on which its period depends?
11
584Dampers are found on bridges
A. to allow natural oscillations to occur
B. to prevent them from swaying due to wind
c. to prevent resonance of frequencies.
D. None of these.
11
585A simple pendulum of length ( 4 mathrm{m} ) is
taken to a height ( R ) (radius of the earth)
from the earth’s surface.The time period of small oscillations of the pendulum is
( left(boldsymbol{g}_{text {surface}}=boldsymbol{pi}^{2} boldsymbol{m} boldsymbol{s}^{-2}right) )
A . 2 s
B. 4 s
( c cdot 8 s )
D. 16 s
11
586Amplitude of oscillation of a particle that executes S.H.M. is 2 cm. Its
displacement from its mean position in a time equal to ( 1 / 6 ) th of its time period
is
A ( cdot sqrt{2} mathrm{cm} )
B. ( sqrt{3} mathrm{cm} )
c. ( 1 / sqrt{2} mathrm{cm} )
D. ( 1 / sqrt{3} mathrm{cm} )
11
587‘The motion of a particle with a restoring force gives oscillatory motion”. Which of the following forces can be a restoring force for the oscillatory motion.
A. Frictional force
B. A constant force
c. A time varying force opposite to direction of motion
D. Force due to a spring
11
588A plane progressive wave is given by ( boldsymbol{y}=25 cos (2 pi t-pi x) ) Then the
amplitude and frequency are respectively
A . 25,100
B. 25,
( c .25 .2 )
D. ( 50 pi, 2 )
11
589A magnet is suspended in such a way that it oscillate it horizontal plane.
It make 20 oscillation per minute at a
place were dip angle is 30 and 15 oscillation per minute t a place were dip angle is ( 60 . ) the ratio of total magnetic field at the two place is
A . 15 oscillations/minute
в. ( 1.7 sqrt{3} )
c. 18 oscillations/minute
D. zero
11
590A particle of mass ( m ) is attached to
three springs ( A, B ) and ( C ) of equal force
constants ( k ) as shown in figure. If the
particle is pushed slightly against the
spring ( C ) and released, the time period
of oscillation is
A ( cdot 2 pi sqrt{frac{m}{k}} )
В ( cdot 2 pi sqrt{frac{m}{2 k}} )
c. ( 2 pi sqrt{frac{m}{3 k}} )
D. ( 2 pi sqrt{frac{3 m}{k}} )
11
591A particle executes SHM with
amplitudes ( 25 mathrm{cm} ) and period 3 seconds. The minimum time required
for it to move between two points 12.5 ( mathrm{cm} ) on either side of the mean position
is
A. ( 0.25 mathrm{sec} )
B . 0.50 sec
c. ( 0.75 mathrm{sec} )
D. ( 1.00 mathrm{sec} )
11
592Find the frequency of osculation of an underdamped harmonic oscillator of
mass ( m ) in terms of its natural
frequency ( omega_{0} ) and damping constant ( gamma ) (where – ( boldsymbol{v} boldsymbol{y} ) is the damping force, ( boldsymbol{v} ) being the velocity)
11
593A particle executes simple harmonic motion between ( boldsymbol{x}=-boldsymbol{A} ) and ( boldsymbol{x}=+boldsymbol{A} )
The time taken for it to go from 0 to ( A / 2 )
is ( T_{1} ) and to ( operatorname{gofrom} A / 2 ) to ( A ) is ( T_{2} ). Then
A ( cdot T_{1}T_{2} )
c. ( T_{1}=T_{2} )
D. ( T_{1}=2 T_{2} )
11
594A particle starts ( S . H . M . ) from the
mean position. Its amplitude is ( A ) and
time period is ( T . ) At the time when its speed is half of the maximum speed, its displacement ( y ) is :
A ( cdot frac{A}{2} )
B. ( frac{A}{sqrt{2}} )
c. ( frac{A sqrt{3}}{2} )
D. ( frac{2 A}{sqrt{3}} )
11
595Part of a simple harmonic motion is
graphed in the figure, where ( y ) is the
displacement from the mean position. The correct equation describing this
S.H.M. is
11
596The diagram shows the displacementtime graph for a vibrating body. Name the type of vibration produced by the vibrating body :11
597The displacement of a particle is given by ( vec{r}=A(vec{i} cos omega t+vec{jmath} sin omega t) . ) The
motion of the particle is:
A. simple harmonic
B. On a straight line
c. on a circle
D. With constant acceleration
11
598A particle moves such that its acceleration is given by ( boldsymbol{a}=-boldsymbol{beta}(boldsymbol{x}-boldsymbol{2}) )
Here ( beta ) is a positive constant and ( x ) is
the position from origin. Time period of oscillations is
A. ( 2 pi sqrt{beta} )
в. ( 2 pi sqrt{frac{1}{beta}} )
( mathbf{c} cdot 2 pi sqrt{beta}+2 )
D. ( 2 pi sqrt{frac{1}{beta+2}} )
11
599A simple pendulum completes 40 oscillation in a minute.Find its (a)
frequency
(b) time period.
11
600Find the time period of the motion of the
particle shown in figure. Neglect the
small effect of the bend near the
bottom.
11
601If a body mass ( 36 g m ) moves with ( mathrm{S}, mathrm{H}, mathrm{M} )
of amplitude ( A=13 ) and period ( T= )
12 ( sec ) At a time ( t=0 ) the displacement
is ( x=+13 c m . ) The shortest time of
passage from ( boldsymbol{x}=+mathbf{6 . 5} mathrm{cm} ) to ( boldsymbol{x}=-mathbf{6 . 5} )
is
( A cdot 4 sec )
B. 2 sec
( c cdot 6 sec )
D. 3 sec
11
602In the figure, the vertical sections of the
string are long. ( A ) is released from rest
from the position shown. Then
A. The system will remain in equilibrium
B. The central block will move down continously
C. The central block will undergo simple harmonic motion
D. The central block will undergo periodic motion but not simple harmonic motion.
11
603The time period of a particle in simple harmonic motion is 8 s. At ( t=0 ), it is at
the mean position. The ratio of the distances travelled by it in the first and second seconds is:
A ( cdot frac{1}{2} )
в. ( frac{1}{sqrt{2}} )
c. ( frac{1}{sqrt{2}-1} )
D. ( frac{1}{sqrt{3}} )
11
604A particle executing S.H.M. completes a distance (taking friction as negligible) in one complete one time period.
A. Four times the amplitude
B. Two times the amplitude
c. one times the amplitude
D. Eight times the amplitude
11
605A particle of mass ( 10 g ) is executing simple harmonic motion with an
amplitude of ( 0.5 m ) and periodic time of ( left(frac{pi}{5}right) s . ) The maximum value of the force acting on the particle is:
A . ( 25 ~ N )
B. ( 5 N )
c. ( 2.5 N )
D. ( 0.5 N )
11
606The number of vibrations made by a
vibrating body in one second is called
its :
A. wavelength
B. time period
c. amplitude
D. frequency
11
607A student performs an experiment for determination of ( left(g=frac{4 pi^{2} l}{T^{2}}right), mid=1 mathrm{m} )
and he commits an error of ( Delta l ) For T he
takes the time of ( n ) oscillations with the
stop watch of least count ( Delta boldsymbol{T} ) and he
commits a human error of 0.1 s. For
which of the following data, the
measurement of ( g ) will be most
accurate?
A. ( Delta L=0.5, Delta T=0.1, n=20 )
B . ( Delta L=0.5, Delta T=0.1, n=50 )
c. ( Delta L=0.5, Delta T=0.01, n=20 )
D. ( Delta L=0.5, Delta T=0.05, n=50 )
11
a bowl of radius b then time period of vibration of ball is ( (boldsymbol{b}>boldsymbol{a}) )
A ( cdot 2 pi sqrt{frac{a}{g}} )
В ( cdot 2 pi sqrt{frac{b-a}{g}} )
( ^{mathrm{c}} cdot 2 pi sqrt{frac{b}{g}} )
D. ( 2 pi sqrt{frac{b+a}{q}} )
11
609A particle of mass ( m ) is executing S.H.M.
of time period ( T, ) and amplitude ( a_{0} . ) The
force on particle at the mean position is:
A ( cdot frac{4 pi^{2} m}{T^{2}} a_{0} )
( ^{text {В } cdot frac{2 pi^{2} m}{T^{2}} a_{0}} )
c. zero
D. ( frac{pi^{2} m a_{0}}{T^{2}} )
11
610What are damped vibrations? How do they differ from free vibrations ? Give one example of each.11
611A boy is executing Simple Harmonic Motion. At a displacement ( x ), its
potential energy is ( E_{1} ) and at a
displacement ( y, ) its potential energy is ( boldsymbol{E}_{2} . ) The potential energy ( boldsymbol{E} ) at
displacement ( (boldsymbol{x}+boldsymbol{y}) ) is:
A ( cdot sqrt{E}=sqrt{E_{1}}-sqrt{E_{2}} )
B. ( sqrt{E}=sqrt{E_{1}}+sqrt{E_{2}} )
c. ( E=E_{1}+E_{2} )
D. ( E=E_{1}-E_{2} )
11
612The two particles are at minimum distance from each other after time, ( t= )
( mathcal{S} )
A .
в. 2.
( c .3 )
D. all of these
11
613In forced oscillation of a particle the amplitude is maximum for a frequency
( omega_{1} ) of force, while the energy is
maximum for a frequency ( omega_{2} ) of the force, then:
A. ( omega_{1}=omega_{2} )
В. ( omega_{1}>omega_{2} )
C. ( omega_{1}omega_{2} ) when damping is large
D. ( omega_{1}<omega_{2} )
11
614The oscillators that can be described in
terms of sine or cosine functions are
called
A. simple harmonic
B. natural
c. sympathetic
D. free
11
615Displacement-time graph depicting an oscillatory motion is
A. cos curve
B. sine curve
c. tangent curve
D. straight line
11
616The ratio of the angular speed of
minutes hand and hour hand of a watch
is:
A . 6: 1
B. 12: 1
c. 1: 6
D. 1: 12
11
617A particle executes ( boldsymbol{S} boldsymbol{H} boldsymbol{M} ) of
amplitude ( 25 c m ) and time period ( 3 s )
What is the minimum time required for the particle to move between two points
( 12.5 mathrm{cm} ) on either side of the mean
position?
A . ( 0.5 s )
B. ( 1.0 s )
c. ( 1.5 s )
D. 2.0
11
618Assertion
In SHM let ( x ) be the maximum speed, ( y )
the frequency of oscillation and ( z ) the maximum acceleration then ( frac{x y}{z} ) is a
constant quantity.
Reason
This is because ( frac{x y}{z} ) becomes a
dimensionless quantity
A. Both Assertion and Reason are correct and Reason is
the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
619The frequency of a sound wave is ( 256 mathrm{Hz} ) and its wavelength is ( 1.2 mathrm{m} ). Calculate its wave velocity.11
620A particle performing SHM has a period of ( 6 s ) and amplitude of ( 8 mathrm{cm} . ) The particle starts from the mean position
and moves towards the positive extremity. At what time will it have the maximum amplitude
A . ( 6 s )
B. 4.5s
( c cdot 1.5 s )
D. 3 s
11
621A particle of mass ( mathrm{m} ) is executing oscillations about the origin on the ( x ) axis. Its potential energy is ( V(x)= )
( k|x|^{3} ) where ( k ) is a positive constant. If
the amplitude of oscillation is a, them its time period T is?
A. proportional to ( frac{1}{sqrt{a}} )
B. Independent of a
c. Proportional to ( sqrt{a} )
D. Proportional to ( a^{3 / 2} / 2 )
11
622The time taken by the bob of a pendulum to complete one oscillation is called its
A. time period
B. amplitude
c. mass
D. frequency
11
623The slope of kinetic energy vs. displacement curve of a particle in motion is:
A. inversely proportional to acceleration of the particle.
B. directly proportional to acceleration of the particle.
c. equal to acceleration of particle.
D. none of the above
11
624In the figure shown, the springs are
connected to the rod at one end and at
the midpoint. The rod is hinged at its
lower end. Rotational SHM of the rod
(Mass ( boldsymbol{m} ), length ( boldsymbol{L} ) ) will occur only if
( mathbf{A} cdot k>m g / 3 L )
В. ( k>2 m g / 3 L )
c. ( k>2 m g / 5 L )
D. ( k>0 )
11
625For a body in S.H.M. the velocity is given by the relation ( boldsymbol{v}=sqrt{144-16 x^{2}} boldsymbol{m} / boldsymbol{s} )
The maximum acceleration is
A ( cdot 12 m / s^{2} )
в. ( 16 m / s^{2} )
( mathrm{c} cdot 36 mathrm{m} / mathrm{s}^{2} )
D. ( 48 mathrm{m} / mathrm{s}^{2} )
11
626Two simple harmonic motions are
represented by the equations. ( boldsymbol{y}_{1}=mathbf{1 0} sin frac{boldsymbol{pi}}{boldsymbol{4}}(1 mathbf{2} boldsymbol{t}+mathbf{1}), boldsymbol{y}_{2}= )
( mathbf{5}(((sin 3 p t+sqrt{3} cos 3 p t) )
The ratio of their amplitudes is
A . 1: 1
B. 1: 2
c. 3: 2
D. 2: 3
11
627The displacement time graph of a particle executing SHM is shown in
figure. Which of the following
statements is/are true?
This question has multiple correct options
A. The velocity is maximum at t=T/2
B. The acceleration is maximum at t=
c. The force is zero at t=37/4
D. The kinetic energy equals the total oscillation energy at ( t=T / 2 )
11
628How much time the man has to board
the boat comfortably during each cycle of up and down motion?
A . 0.585 s
в. 1.17 s
( c cdot 2.33 mathrm{s} )
D. 0.293 s
11
629A hydrogen atom has mass ( 1.68 times ) ( 10^{-27} mathrm{kg} . ) When attached to a certain
massive molecule it oscillates with a
frequency ( 10^{14} mathrm{Hz} ) and with an
amplitude ( 10^{-9} mathrm{cm} . ) Find the force
acting on the hydrogen atom.
B . ( 3.31 times 10^{-9} ) N
c. ( 4.42 times 10^{-9} ) N
D. ( 6.63 times 10^{-9} ) N
11
630On suspending a mass M from a spring of force constant K,frequency of vibration ( f ) is obtained If a second spring as shown in the figure. is arranged then the frequency will be :
A ( . f sqrt{2} )
B. ( f / sqrt{2} )
( c . ) २
D.
11
631The amplitude of a particle executing
SHM about O is 10 cm. Then:
This question has multiple correct options
A. When the K.E. is 0.64 of its max. K.E. its displacement is ( 6 mathrm{cm} ) from 0 .
B. When the displacement is 5 cm from 0 its K.E. is 0.75 of its max.P.E.
C. Its total energy at any point is equal to its maximum
K.E.
D. Its velocity is half the maximum velocity when its displacement is half the maximum displacement.
11
632The oscillations represented by curve 1
in the graph are expressed by equation
( x= ) Asinwt. The equation for the
oscillations represented by curve 2 is expressed as:
A. ( x=2 A sin (omega t-pi / 2) )
B. ( x=2 A sin (omega t+pi / 2) )
c. ( x=-2 operatorname{Asin}(omega t-pi / 2) )
D. ( x=operatorname{Asin}(omega t-pi / 2) )
11
633A particle performing SHM with a frequency of ( 5 mathrm{Hz} ) and amplitude ( 2 mathrm{cm} ) is initially in the positive extreme position. The equation for its displacement is
A. ( x=0.02 sin 10 pi t mathrm{m} )
B. ( x=0.02 sin 5 pi t mathrm{m} )
c. ( x=0.02 cos 10 pi t mathrm{m} )
D. ( x=0.02 cos 5 pi t mathrm{m} )
11
634The displacement of a particle in S.H.M.
is indicated by equation ( boldsymbol{y}= )
( 10 sin (20 t+Omega / 3) ) where ( y ) is in
metres. The value of time period of vibration will be (in seconds):
A . ( 10 / pi )
в. ( pi / 10 )
c. ( 2 pi / 10 )
D. ( 10 / pi 2 )
11
635Assertion
The time period of a simple pendulum is independent of its length.
Reason
The length of a pendulum is the distance between point of suspension
and centre of the bob
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
636A particle moves under the force
( boldsymbol{F}(boldsymbol{x})=left(boldsymbol{x}^{2}-boldsymbol{6} boldsymbol{x}right) boldsymbol{N}, ) where ( boldsymbol{x} ) is in
meters. Show that for small
displacements from the origin the force constant in the simple harmonic motion is approximately 6
11
637A block performs simple harmonic
motion with equilibrium point ( boldsymbol{x}=mathbf{0} )
Graph of acceleration of the block as a
function of time is shown. Which of the
following statement is correct about the
block?
A. Displacement from equilibrium is maximum at ( t=4 s )
B. Speed is maximum at ( t=4 s )
C. Speed is maximum at ( t=2 s )
D. Speed is maximum at ( t=3 s )
11
638Two particles are in SHM in parallel straight lines close to each other. Amplitude ( A ) and time period ( T ) of both
the particles are equal. At ( t=0, ) one
particle is at displacement ( boldsymbol{x}_{mathbf{1}}=+boldsymbol{A} ) and other at ( x_{2}=-frac{A}{2} ) an they are
approaching towards each other, after what time they will cross each other?
A. ( T / 3 )
в. ( T / 4 )
( mathrm{c} cdot 5 T / 6 )
D. ( T / 6 )
11
639The force which tries to bring the body back to its mean position is called
A. deforming force
B. restoring force
c. gravitational force
D. buoyant force
11
640A body describing SHM has a maximum
acceleration of ( 8 pi mathrm{m} / mathrm{s}^{2} ) and a
maximum speed of ( 1.6 mathrm{m} / mathrm{s} ). Find the period ( T ) and the amplitude ( A )
11
641Give two practical applications of simple harmonic motion.11
642represents the position-time graph for a
spring-mass system oscillating with simple harmonic motion. The colored, dashed graphs represent shapes of possible velocity time graphs
for the same motion.

The vertical axis stands for position or
velocity, but the scaling does not matter. The time axis is the same for all
graphs.
Which colored graph best represents
the possible velocity for the mass in
this spring-mass system?
A. Red
B. Blue
c. Green
D. The velocity graph is the same as the position graph
E. All three colored graphs are equally possible

11
643The potential energy of a particle
varies with distance ( x ) as shown in the
graph. The force acting on the particle is
zero at:
( A ).
B
( c . ) В and ( c )
D. A and
11
644The potential energy of a particle is directly proportional to its linear displacement from its mean position. Then, the particle performs a
A. Retarding straight line motion
B. Damped SHM
c. Linear SHM
D. Angular SHM
11
645The period of small oscillations is
A ( cdot pi a sqrt{frac{m}{C}} )
В. ( pi a sqrt{frac{2 m a}{c}} )
C ( cdot 2 pi sqrt{frac{2 m a^{3}}{C}} )
D. ( 2 pi a sqrt{frac{m a}{C}} )
11
says that
A. the direction of force is sometimes opposite to the direction of body’s motion
B. the force is in the same direction to the body’s motion
c. the force is in the opposite direction to the body’s motion
D. None of these
11
647The amplitude and the periodic time of a SHM are ( 5 c m ) and ( 6 s ) respectively. At a
distance of ( 2.5 mathrm{cm} ) away from the mean position, the phase will be
( ^{A} cdot frac{pi}{3} )
в.
c.
D. ( frac{5 pi}{12} )
11
648A particle of mass ( m ) is moving along the X-axis under the potential ( U(x)= ) ( frac{k x^{2}}{2}+lambda ) where ( k ) and ( lambda ) are positive constants of appropriate dimensions. The particle is slightly displaced from its equilibrium position. The particle oscillates with the angular frequency
( (omega) ) given by
A ( cdot_{3} frac{k}{m} )
в. ( 3 frac{m}{k} )
c. ( sqrt{frac{k}{m}} )
D. ( sqrt{3 frac{m}{k}} )
E ( cdot sqrt{3 frac{k}{m}} )
11
649A simple harmonic motion has an amplitude ( A ) and time period ( T . ) Find the time required by it to travel directly from ( boldsymbol{x}=boldsymbol{A} ) to ( boldsymbol{x}=boldsymbol{A} / mathbf{2} )11
650A plot of potential energy v/s kinetic energy of a particle executing SHM gives a straight line
A. passing through the origin
B. with positive slope
c. with intercepts on both the axes
D. parallel to either of the axes
11
651The period of oscillation of a simple pendulum of length lis given by ( boldsymbol{T}= ) ( 2 pi sqrt{l / g} . ) The length lis about ( 10 mathrm{cm} ) and
is known to ( 1 mathrm{mm} ) accuracy. The period of oscillation is about 0.5 s. The time of 100 oscillations has been measured
with a stop watch of 1 s resolution. Find
the percentage error in the determination of ( mathfrak{g} )
11
652A particle executes simple harmonic
motion with a frequency ( v ). The
frequency with which the kinetic energy oscillates is
( mathbf{A} cdot v / 2 )
B. ( v )
c. ( 2 v )
D. Zero
11
653The amplitude of a damped oscillator becomes ( left(frac{1}{3}right) r d ) in ( 2 s . ) If its amplitude ( operatorname{after} 6 s operatorname{in} frac{1}{n} ) times the original
amplitude, the value of ( n ) is
( A cdot 3^{2} )
B. ( 3 sqrt{2} )
( c cdot 3^{3} )
D. ( 2^{3} )
11
654If a simple harmonic motion is represented by ( frac{d^{2} x}{d t^{2}}+alpha x=0, ) its time period is then
A. ( 2 pi sqrt{alpha} ).
. ( sqrt{sqrt{alpha}} ). ( alpha ).
в. ( 2 pi alpha )
c. ( frac{2 pi}{sqrt{alpha}} )
D. ( frac{2 pi}{alpha} )
11
655By suspending a mass of ( 0.50 mathrm{kg} ), a spring is stretched by ( 8.20 mathrm{m} . ) If a mass of ( 0.25 mathrm{kg} ) is suspended, then its period of oscillation will be:
(Take ( g=10 m s^{-2} ) )
A . 0.137 s
B. 0.328 s
c. 0.628 s
D. 1.000
11
656Which of the following equations represents a particle performing simple harmonic motion
A ( cdot x=3 )
B. ( x=4 sin 2 t )
( c cdot x=1 / t )
D. ( x=3 log 2 t )
11
657The mean value of velocity vector projection average over ( 3 / 8 ) th of a period after the start is
A ( cdot frac{2 sqrt{2} A omega}{pi} )
B. ( frac{2 A omega}{3 sqrt{2 pi}} )
c. ( frac{A omega}{3 pi} )
D. ( frac{2 sqrt{2} A omega}{3 pi} )
11
658The acceleration (a) of SHM at mean
position is :
A. zero
B. ( propto x )
( c cdot propto x^{2} )
D. None of these
11
659A rigid body rotates about a fixed axis with variable angular velocity equal to ( (a b t) ) at ( t ) where a and ( b ) are
constants. The angle through which it rotates before it comes to rest is
A ( cdot frac{a^{2}}{b} )
в. ( frac{a^{2}}{2 b} )
c. ( frac{a^{2}}{4 b} )
D. ( frac{a^{2}}{2 b^{2}} )
11
660A particle executes ( S H M ) of period
( 1.2 mathrm{sec} ) and amplitude ( 8 mathrm{cm} . ) Find the
time it takes to travel ( 3 mathrm{cm} ) from the
positive extremity or its oscillation.
( left[cos ^{-1}(5 / 8)=0.9 r a dright] )
A. 0.28 sec
B. 0.32 sec
c. 0.17 sec
D. 0.42 sec
11
661In a simple harmonic motion
A. the maximum potential energy equals the maximum kinetic energy
B. the minimum potential energy equals the minimum kinetic energy
C. the minimum potential energy equals the maximum kinetic energy
D. the maximum potential energy equals the minimum kinetic energy
11
662A particle executes simple harmonic
motion with a frequency ( f ). The frequency with which the potential energy oscillates is:
( A cdot f )
B. ( frac{f}{2} )
c. ( 2 f )
D. zero
11
663Two wave are represented by equation
( boldsymbol{y}_{1}=boldsymbol{a} sin omega t ) and ( boldsymbol{y}_{2}=boldsymbol{a} cos omega boldsymbol{t} . ) Then
the first wave:
A. leads the second by ( pi )
B. lags the second by ( pi )
c. leads the second by ( frac{pi}{2} )
D. lags the second by ( frac{pi}{2} )
11
664Match List – I (Event) with List – II (Order
of the time interval for happening of the
event) and select the correct option from the options given below the lists.
List – 1
(a) Rotation period of
(i) earth
Revolution period of
(ii)
(b) earth
( (c) )
Period of a light
(iii) wave
( (d) )
Period of a sound
iv wave
A ( cdot(a)-(i),(b)-(i i),(c)-(i i i),(d)-(i v) )
B. (a)-(ii), (b)-(i), (c)-(iv), (d)-(iii)
( c cdot(a)-(i),(b)-(i i),(c)-(i v),(d)-(i i i) )
D. (a)-(ii), (b)-(i), (c)-(iii), (d)-(iv)
11
665A particle executing SHM has a
maximum speed of ( 0.5 m s^{-1} ) and
maximum acceleration of ( 1 m s^{-2} )
The angular frequency of oscillation is:
A ( cdot 2 r a d s^{-1} )
B . 0.5 rads( ^{-1} )
C ( .2 pi r a d s^{-1} )
D. ( 0.5 pi r a d s^{-1} )
11
666Mention any two characteristics of SHM (Simple Harmonic Motion).11
667The phase angle between the projections of uniform circular motion
on two mutually perpendicular diameter is
A . ( pi )
в. ( 3 pi / 4 )
c. ( pi / 2 )
D. zero
11
668The displacement (in ( mathrm{m} ) ) of a particle of mass 100 gram from its equilibrium position is given by ( boldsymbol{y}=mathbf{0 . 0 1} sin 2 pi(t+ )
0.4). Select the correct option(s):
This question has multiple correct options
A. The time period of motion is 1 sec.
B. The time period of motion is ( frac{1}{7.5} ) sec
c. The maximum acceleration of the particle is ( 0.04 pi^{2} m / s^{2} )
D. The force acting on the particle is zero when the displacement is 0.05m
11
669A particle executes simple harmonic oscillation
with an amplitude a. The period of oscillation is
T. The minimum time taken by the
particle to travel half of the amplitude from the equilibrium position is:
A. ( T / 2 )
в. ( T / 4 )
( c cdot T / 8 )
D. T/12
11
670( x-t ) equation of a particle in SHM is,
( boldsymbol{x}=mathbf{4}+mathbf{6} sin boldsymbol{pi} boldsymbol{t} )
Match the following tables corresponding to time taken in moving from:
11
671A toy train rotates about a circle of
radius ( 50 mathrm{cms}, 10 ) times in 2 minutes.
What is the frequency of the train
A. 5 per second
B. 12 per second
c. ( 1 / 12 ) per second
D. ( 1 / 5 ) per second
11
672Assertion
In case of oscillatory motion the average speed for any time interval is always greater than or equal to its average velocity
Reason
Distance travelled by a particle cannot be less than its displacement.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
673Which of the following functions represent a simple harmonic motion?
( mathbf{A} cdot sin omega t-cos omega t )
B. ( sin ^{2} omega t )
( mathbf{c} cdot sin omega t+sin ^{2} omega t )
D. ( sin omega t-sin ^{2} omega t )
11
674If a simple harmonic motion is represent by ( frac{d^{2} x}{d t^{2}}+a x=0, ) its time period is
A ( cdot frac{2 pi}{alpha} )
в. ( frac{2 pi}{sqrt{alpha}} )
( c cdot 2 pi alpha )
D. ( 2 pi sqrt{alpha} )
11
675The period of pendulum depends upon
A. mass
B. length
c. amplitude
D. energy
11
676One end of an ideal spring is fixed to a
wall at origin ( O ) and axis of spring is
parallel to x-axis. A block of mass ( boldsymbol{m}= )
1 kg is attached to free end of the
spring and it is performing SHM. Equation of position of the block in coordinate system shown in figure is
( boldsymbol{x}=mathbf{1 0}+mathbf{3} sin (mathbf{1 0} boldsymbol{t}) . ) Here, ( boldsymbol{t} ) is in second
and ( x ) in cm. Another block of mass
( M=3 k g, ) moving towards the origin
with velocity ( 30 mathrm{cm} / mathrm{s} ) collides with the block performing SHM at ( t=0 ) and gets
stuck to it. Calculate new amplitude of oscillations
11
677In a damped harmonic oscillator, periodic oscillations have
amplitude.
B. Suddenly increasing
c. suddenly decreasing
11
678Calculate the velocity of the bob of a
simple pendulum at its mean position if it is able to rise to a vertical height of ( 10 mathrm{cm} . ) Given: ( g=980 mathrm{cms}^{-2} )
11
679State the differential equation of linear simple harmonic motion. Hence obtain
the expression for acceleration, velocity and displacement of a particle performing linear simple harmonic motion.

A body cools from ( 80^{circ} mathrm{C} ) to ( 70^{circ} mathrm{C} ) in 5
minutes and to ( 62^{circ} C ) in the next 5
minutes. Calculate the temperature of the surroundings.

11
680Assertion
For a particle performing SHM, its speed decreases as it goes away from the mean position.
Reason
In SHM, the acceleration is always
opposite to the velocity of the particle.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Both Assertion and Reason are incorrect
11
681The motion of a particle is given by ( boldsymbol{x}= )
( a sin omega t+b cos omega t . ) The motion of the
particle is:
A. Not simple harmonic
B. Simple harmonic with amplitude ( (A-B) / 2 )
C. Simple harmonic with amplitude ( (A+B) / 2 )
D. Simple harmonic with amplitude ( sqrt{A^{2}+B^{2}} )
11
682The displacement ( y ) of a particle executing periodic motion is given by ( y=4 cos ^{2}left(frac{1}{2} tright) sin (1000 t) . ) This
expression may be considered to be a result of the superposition of independent harmonic motions
A. two
B. three
c. four
D. five
11
683Undamped oscillations are practically impossible because
A. there is always loss of energy.
B. there is no force opposing friction.
C. energy is not conserved in such oscillations
D. None of these.
11
684Assertion : In damped oscillations, the energy of the system is dissipated continuously. Reason: For the small damping, the oscillations remain approximately periodic.
A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true and reason is not the correct explanation of assertion.
c. If assertion is true but reason is false
D. If both assertion and reason are false
11
685How much energy has been lost during these four oscillations?
A . 0.31
B. 0.41
c. 0.51
D. 0.39
11
686The position and velocity of a particle executing simple harmonic motion at ( t=0 ) are given by ( 3 mathrm{cm} ) and ( 8 mathrm{cm} / mathrm{s} )
respectively. If the angular frequency of the particle is ( 2 r a d / s ), then the amplitude of oscillation, in centimeters
is?
A . 3
B. 4
c. 5
D. 6
( E )
11
687The direction of velocity of a pendulum bob at the right extreme position is:
A. towards right
B. towards north
c. towards the centre
D. towards left
11
688The amplitude of a particle executing
SHM about 0 is ( 10 mathrm{cm} . ) Then:
A. when the KE is 0.64 times of its maximum KE, its displacement is 6 cm from 0
B. its speed is half the maximum speed when its displacement is half the maximum displacement
( c . ) Both
(a) and
(b) are correct
D. Both (a) and
(b) are wrong
11
689A particle is acted upon by a force given
by ( boldsymbol{F}=-boldsymbol{alpha} boldsymbol{x}^{3}-boldsymbol{beta} boldsymbol{x}^{4} ) where ( boldsymbol{alpha} ) and ( boldsymbol{beta} ) are
positive constants. At the point ( x=0 )
the particle is
A. In stable equilibrium
B. In unstable equilibrium
c. In neutral equilibrium
D. Not in equilibrium
11
690The angle between the instantaneous velocity and acceleration of a particle executing SHM is
A. zero or ( pi )
В. ( pi / 2 )
c. zero
D.
11
691A simple pendulum is oscillating with
amplitude ( A ) and angular frequency ( omega )
At displacement ( x ) from mean position,
the ratio of kinetic energy to potential energy is
A ( cdot frac{x^{2}}{A^{2}-x^{2}} )
B. ( frac{x^{2}-A^{2}}{x^{2}} )
c. ( frac{A^{2}-x^{2}}{x^{2}} )
D. ( frac{A-x}{x} )
11
692Two spring of force constant ( 300 mathrm{N} / mathrm{m} ) (spring ( A ) ) and ( 400 mathrm{N} / mathrm{m} ) (spring ( mathrm{B} ) ) are joined together in series. The combination is compressed by ( 8.75 mathrm{cm} ) The ratio of energy stored in ( A ) and ( B ) is
( underline{E}_{boldsymbol{B}_{boldsymbol{B}}} )
A ( cdot frac{4}{3} )
в. ( frac{16}{9} )
( c cdot frac{3}{4} )
D. ( frac{9}{16} )
11
693For a particle performing linear S.H.M. Its average speed over one oscillation is ( (a=a m p l i t u d e text { of } S . H . M, n= ) frequency of oscillation)
A . ( 2 a n )
B. 4an
c. ( 6 a n )
D. ( 8 a n )
11
694The angular frequency of the damped
oscillator is given by ( omega= ) ( sqrt{left(frac{k}{m}-frac{r^{2}}{4 m^{2}}right)} ) where ( k ) is the spring
constant, ( m ) is the mass of the oscillator
and ( r ) is the damping constant. If the ratio ( frac{r^{2}}{m k} ) is ( 8 % ), the changed in time
period compared to the undamped oscillator is approximately as follows:
A. Increases by ( 1 % )
B. Decreases by 1%
c. Decreases by ( 8 % )
D. increases by 8%
11
695The displacement of a particle in
S.H. ( M . ) is indicated by equation ( y= )
( mathbf{1 0} sin (mathbf{2 0 t}+boldsymbol{pi} / mathbf{3}) ) where ( boldsymbol{y} ) is in
metres. The value of maximum velocity
of the particle will be :
A . ( 100 mathrm{m} / mathrm{sec} )
B . 150 m/sec.
c. ( 200 mathrm{m} / mathrm{sec} )
D. 400 ( mathrm{m} / mathrm{sec} )
11
696For any SHM, amplitude is ( 6 mathrm{cm} ). If instantaneous potential energy is half the total energy then distance of particle from its mean position is
A. 3 cm
B. ( 4.2 mathrm{cm} )
c. ( 5.8 mathrm{cm} )
D. 6 cm
11
697A horizontal rod of length L and mass ( mathrm{m} ) lying on the floor is fixed at one end and a force ( F ) is applied at an angle ( theta ) with the horizontal. The torque experienced by the rod is
( mathbf{A} cdotleft(m L^{2} alpharight) / 12 )
В. ( left(m L^{2} alpharight) / 3 )
c. ( left(m L^{2} alpharight) / 4 )
D. ( left(m L^{2} alpharight) / 2 )
11
698A particle executes SHM on a straight line. At two positions it’s velocity ( u ) and ( boldsymbol{v} ) while acceleration, ( boldsymbol{alpha} ) and ( boldsymbol{beta} )
respectively ( [beta>alpha>0] . ) the distance
between the these two positions is
A ( cdot frac{u^{2}+v^{2}}{alpha+beta} )
в. ( frac{u^{2}-v^{2}}{alpha+beta} )
c. ( frac{u^{2}-v^{2}}{beta-alpha} )
D. ( frac{u^{2}+v^{2}}{beta-alpha} )
11
sornetıries consider a thingy aldacried
to a horizontal spring and moving horizontally on a frictionless surface,
instead of the hanging thingy that we have been looking at. Suppose that the
two springs and the two thingies are
two systems are significantly different
in other respects and decide which one
of the following statements is true.
A. The systems have different periods because their motions are aligned differently with the gravitational field.
B. The hanging system has a slightly smaller period because the weight of the spring has to be accounted for.
C. The hanging system has a slightly larger period because the weight of the spring has to be accounted for.
D. The two systems have identical periods, no matter what the weight of the spring is.
11
700Two blocks ( P ) and ( Q ) of masses ( 0.3 k g ) and 0.4 kg respectively are stuck to each other by some weak glue as shown in the figure. They hang together at the end of a spring with a spring constant ( boldsymbol{K}=mathbf{2 0 0} boldsymbol{N} boldsymbol{m}^{-1} . ) If the block ( boldsymbol{Q} )
suddenly falls free due to the failure of glue, find
(i) period of SHM of block ( boldsymbol{P} )
(ii) The amplitude of its SHM
(iii) The total energy of oscillation of the
system.
11
701For what instant of time, does potential energy becomes equal to kinetic energy for a particle executing SHM with a time period ( T )
A. ( T / 4 )
в. ( T / 8 )
c. ( T / 2 )
D. ( T )
11
702A particle executes ( S H M ) with time period ( T ) and amplitude ( A ), The maximum possible average velocity in time ( T / 4 ) is
A ( cdot frac{2 A}{T} )
в. ( frac{4 A}{T} )
c. ( frac{8 A}{T} )
D. ( frac{4 sqrt{2 A}}{T} )
11
703A simple harmonic motion has an
amplitude ( A ) and time period ( T ). Find the time required by it to travel directly from ( boldsymbol{x}=mathbf{0} ) to ( boldsymbol{x}=frac{boldsymbol{A}}{mathbf{2}} )
11
704The displacement – time graph for a
particle executing SHM is as shown in
figure
Which of the following statement is
correct?
A ( cdot ) the velocity of the particle is maximum at ( t=frac{3}{4} T )
B. The velocity of the particle is maximum at ( t=frac{T}{2} )
C the acceleration of the particle is maximum at ( t=frac{T}{4} )
D. The acceleration of the particle is maximum at ( t=frac{3}{4} T )
11
705A particle is executing SHM with amplitude ( A ) and has maximum
vekocity ( v_{0} . ) Find its speed when it is located at distance of ( frac{A}{2} ) from position.
11
706Two particles ( P ) and ( Q ) describe SHM of same amplitude a and frequency along the same straight line. The
maximum distance between the two
particles is ( a sqrt{2} . ) The initial phase difference between the particle is
( mathbf{A} cdot pi / 3 )
в. ( pi / 2 )
c. ( pi / 6 )
D. zero
11
707Which is the correct representation of
the net force ( f_{n e t} ) on the mass?
(k is the constant of oscillation and ( x ) is
position)
A ( cdot f_{n e t}=-k x+b v )
B. ( f_{n e t}=k x+b v )
C ( cdot f_{n e t}=-k x-b v )
( mathbf{D} cdot f_{n e t}=k x-b v )
11
708How long will it be moving until it stops for the first time?
A ( cdot t=2 frac{pi}{omega} )
В ( cdot t=3 frac{pi}{omega} )
c. ( t=4 frac{pi}{omega} )
D・ ( t=frac{pi}{omega} )
11
709The diagram shows the displacement-
time graph for a vibrating body. Give an
example of a body producing such
vibrations :
11
710A body executing SHM has its velocity ( 10 c m / s ) and ( 7 c m / s ) when its
displacements from mean position are
( 3 c m ) and ( 4 c m ) respectively. The length of path is
( mathbf{A} cdot 10 mathrm{cm} )
B. ( 9.5 mathrm{cm} )
c. ( 4 c m )
D. ( 11.36 mathrm{cm} )
11
711A body of mass ( 1 / 4 mathrm{kg} ) is in S.H.M and its displacement is given by the relation ( boldsymbol{y}=mathbf{0 . 0 5 operatorname { s i n }}left(mathbf{2 0 t}+frac{boldsymbol{pi}}{mathbf{2}}right) mathrm{m} . ) If ( boldsymbol{t} ) is in
seconds, the maximum force acting on the particle is:
A . 5 N
B. 2.5 N
c. 10 N
D. 0.25 N
11
712( ln S H M ) restoring force is ( F=-k x )
where ( k ) is force constant, ( x ) is
displacement and ( a ) is amplitude of
motion, then total energy depends upon
A. ( k, a ) and ( m )
в. ( k, x, m )
c. ( k, a )
D. ( k, x )
11
713At resonance, the amplitude of forced oscillations is
A. minimum
B. maximum
c. zero
D. none of these
11
714A particle of mass ( 0.3 mathrm{kg} ) is subjected to a force ( boldsymbol{F}=-boldsymbol{k} boldsymbol{x} ) with ( mathbf{k}=15 mathrm{N} / mathrm{m} . ) What
will be its initial acceleration if it is
released from a point ( x=20 mathrm{cm} ? )
11
715A comparison of the plots of the magnitude of acceleration – time graph and displacement – time graph for a particle executing SHM with angular velocity 2 rad/s reveals
A. Both the curves overlap exactly with their magnitudes
B. The curve appear complementary to each other
C. The time periods calculated using these plots are identical
D. The time period calculated in both the plots are different
11
716The diagram shows the displacement-
time graph for a vibrating body. Why is the amplitude of the wave gradually
decreasing?
11
717The figure shows the displacementtime graph of a particle executing SHM. If the time period of oscillation is ( 2 s ) then the equation of motion is given by
( boldsymbol{x}=boldsymbol{z} sin (boldsymbol{pi} boldsymbol{t}+boldsymbol{pi} / boldsymbol{6}) . ) Find ( boldsymbol{z} )
11
718The disk has a weight of ( 100 mathrm{N} ) and rolls without slipping on the horizontal surface as it oscillates about its
equilibrium position. If the disk is displaced, by rolling it counterclockwise 0.4 rad, determine the
equation which describes its oscillatory motion when it is released.
A ( cdot theta=-0.2 cos (16.16 t) )
B ( cdot theta=0.2 cos (16.16 t) )
c. ( theta=-0.4 cos (16.16 t) )
11
719When a spring is extended by ( 2 mathrm{cm} ) energy stored is 100 J. When extended
by further ( 2 mathrm{cm}, ) the energy increases by
A . ( 400 J )
B. ( 300 J )
c. ( 200 J )
D. ( 100 J )
11
720A steel ball of mass ( 0.5 mathrm{kg} ) is dropped from a height of ( 4 mathrm{m} ) on to a horizontal heavy steel slap. the strile the slap and reounds to its original height.
(a) calculate the impulse delivered to the ball during impact
(b) if the ball is in contact with the slab
for ( 0.002, ) find the average reaction
force on the ball during impact.
11
721A block rest on a horizontal table which
is executing SHM in the horizontal with
an amplitude ( a ) if the coefficient of friction is ( mu, ) then the block just start to slip when the frequency of oscillation is
A ( cdot frac{1}{2 pi} sqrt{frac{mu g}{a}} )
В ( cdot 2 pi sqrt{frac{a}{mu g}} )
( ^{mathrm{C}} cdot frac{1}{2 pi} sqrt{frac{a}{mu g}} )
D. ( sqrt{frac{a}{mu g}} )
11
722A mass of ( 5 mathrm{kg} ) is suspended from a spring of stiffness ( 46 mathrm{kN} / mathrm{m} . ) A dashpot is fitted between the mass and the
support with a damping ratio of 0.3 Calculate the damped frequency.
A. ( 14.56 mathrm{Hz} )
B. 14.28 Hz
c. ( 14.42 mathrm{Hz} )
D. 14.14 нz
11
723The motion of a pendulum is an example of :
A. translatory motion
B. rotational motion
c. oscillatotry motion
D. curvilinear motion
11
724Which of the following expressions does not represent simple harmonic motion?
A ( . x= ) Acoswt ( + ) Bsinwt
В. ( F=sqrt{k y} )
c. ( F=k y )
D. none of these
11
725Which of the following functions represents a simple harmonic oscillation?
A. sinwt – coswt
B. ( sin ^{2} omega t )
c. sinwt ( +sin 2 omega t )
D. ( sin omega t-sin 2 omega t )
11
726A bob is suspended by a string of length
I. The minimum horizontal velocity imparted to the ball for reaching it to the height of suspension is
( mathbf{A} cdot sqrt{l / g} )
B . ( sqrt{2 g l} )
c. ( sqrt{g / l} )
D. ( 2 sqrt{g l} )
11
727A particle execute ( S H M ) from the
mean position. its amplitude is ( A ) its time period ( T . ) At what displacement its
speed is half of its maximum speed?
A ( cdot frac{sqrt{3} mathrm{A}}{2} )
B. ( frac{sqrt{2}}{3} mathrm{A} )
( c cdot frac{2 A}{sqrt{3}} )
( D cdot frac{3 A}{sqrt{2}} )
11
728A particle is executing SHM with time
period T. Starting from mean position, time taken by it to complete ( 5 / 8 ) oscillations, is
11
729The time taken by a particle performing
S.H.M. to pass from point ( boldsymbol{A} ) to ( boldsymbol{B} ) where its velocities are same is 2 seconds.
After another 2 seconds it returns to ( mathrm{B} )
The time period of oscillation is (in seconds):
A .2
B. 4
( c cdot 6 )
( D )
11
730A ( 1 mathrm{kg} ) mass executes SHM with an amplitude ( 10 mathrm{cm}, ) it takes ( 2 pi ) seconds to
go from one end to the other end. The
magnitude of the force acting on it at any end is :
A . ( 0.1 mathrm{N} )
B. 0.2 N
c. ( 0.5 mathrm{N} )
D. 0.05 N
11
731A body is executing simple harmonic motion. At a displacement ( x ), its
potential energy is ( E_{1} ) and at
displacement ( y, ) its potential energy is
( boldsymbol{E}_{2} ) The potential energy ( mathrm{E} ) at a displacement ( (x+y) ) is
A ( cdot E_{1}+E_{2} )
B. ( sqrt{E_{1}^{2}+E_{2}^{2}} )
c. ( E_{1}+E_{2}+2 sqrt{E_{1} E_{2}} )
D. ( sqrt{E_{1} E_{2}} )
11
732Assertion
Graph between potential energy of a spring versus the extension or compression of the spring is a straight
line
Reason
Potential energy of a stretched or
compressed spring is proportional to
square of extension or compression
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
11
733Two masses ( m_{1} ) and ( m_{2} ) are suspended
together by a massless spring of spring
constant ( k ) as shown in the figure. When
the masses are in equilibrium, ( m_{1} ) is
removed without disturbing the system.
Find the angular frequency and
amplitude of oscillation of ( boldsymbol{m}_{2} )
A ( cdot sqrt{frac{k}{3 m_{2}}} )
B. ( sqrt{frac{k}{m_{2}}} )
c. ( sqrt{frac{k}{2 m_{2}}} )
D. ( sqrt{frac{k}{4} m_{2}} )
11
734A particle performs linear S.H.M. At a particular instant, velocity of the
particle is ( ^{prime} u^{prime} ) and acceleration is ( ^{prime} alpha^{prime} )
while at another instant velocity is ( ^{prime} v^{prime} )
and acceleration is ( ^{prime} boldsymbol{beta}^{prime}(mathbf{0}<boldsymbol{alpha}<boldsymbol{beta}) . ) The
distance between the two positions is
A ( cdot frac{u^{2}-v^{2}}{alpha+beta} )
в. ( frac{u^{2}+v^{2}}{alpha+beta} )
c. ( frac{u^{2}-v^{2}}{alpha-beta} )
D. ( frac{u^{2}+v^{2}}{alpha-beta} )
11
735A body is executing SHM. If the force
acting on the body is ( 6 mathrm{N} ) when the displacement is ( 2 mathrm{cm}, ) then the force acting on the body when the displacement is ( 3 mathrm{cm} ) in newton is:
A. 6 N
B. 9 N
( c .4 mathrm{N} )
D. ( sqrt{6} ) N
11
736The displacement of a particle of mass
( 3 g m ) executing simple harmonic motion is given by ( y=3 sin (0.2 t) ) in ( s )
units. The kinetic energy of the particle at a point which is at a distance equal to ( frac{1}{3} ) of its amplitude from its mean position is
A ( cdot 12 times 10^{-3} J )
( J )
B . ( 25 times 10^{-3} J )
c. ( 0.48 times 10^{-3} J )
D. ( 0.24 times 10^{-3} mathrm{J} )
11
737The displacement of a particle in SHM
is indicted by equation ( boldsymbol{y}= ) ( 10 sin left(20 t+frac{pi}{3}right) ) where ( y ) is in metres.
The value of the maximum velocity of the particle will be?
A. ( 100 mathrm{m} / mathrm{s} )
в. ( 150 mathrm{m} / mathrm{s} )
c. ( 200 m / s )
D. ( 400 mathrm{m} / mathrm{s} )
11
738For a particle performing SHM:
A. The kinetic energy is never equal to the potential
energy
B. The kinetic energy is always equal to the potential energy
C. The average kinetic energy in one time period is equal to the average potential energy in this period.
D. The average kinetic energy in any time interval is never equal to average potential energy in that interval.
11
739If at any instant of time the
displacement of a harmonic oscillator is ( 0.02 mathrm{m} ) and its acceleration is ( 2 mathrm{ms}^{-2} )
its angular frequency at that instant will be