JEE Main & Advanced Physics Wave Mechanics Question Bank

Self Evaluation Test - Oscillations Total Questions - 100

1)

A particle performs SHM in a straight line. In the first second, starting from rest, it travels a distance a and in the next second it travels a distance b in the same direction. The amplitude of the SHM is

A)
\[a-b\]

B)
\[\frac{2a-b}{3}\]

C)
\[\frac{2{{a}^{2}}}{3a-b}\]

D)
None of these
View Solution
2)

A 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 given by:

A)
\[\sin \,t+\frac{1}{2}\cos \,2t\]

B)
\[\cos t-\frac{1}{2}\sin \,2t\]

C)
\[\sin t-\frac{1}{2}\sin \,2t\]

D)
\[\sin t+\frac{1}{2}\sin \,2t\]
View Solution
3)

Part 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

A)
\[y=4\cos (0.6t)\]

B)
       \[y=2\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\]

C)
\[y=4\sin \left( \frac{10}{3}t+\frac{\pi }{2} \right)\]

D)
\[y=2\cos \left( \frac{10}{3}t+\frac{\pi }{2} \right)\]
View Solution
4)

If a is the amplitude of SHM, then K.E. is equal to the P.E. at............ distance from the mean position.

A)
\[\frac{a}{\sqrt{2}}\]

B)
\[\frac{a}{2}\]

C)
\[\frac{a}{4}\]

D)
\[a\]
View Solution
5)

Which of the following is true about total mechanical energy of SHM?

A)
It is zero at mean position.

B)
It is zero at extreme position.

C)
It is always zero.

D)
It is never zero.
View Solution
6)

In S.H. M. the ratio of kinetic energy at mean position to the potential energy when the displacement is half of the amplitude is

A)
\[\frac{4}{1}\]

B)
\[\frac{2}{3}\]

C)
\[\frac{4}{3}\]

D)
\[\frac{1}{2}\]
View Solution
7)

Starting from the 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)
\[\frac{1}{6}s\]

B)
\[\frac{1}{4}s\]

C)
\[\frac{1}{3}s\]

D)
\[\frac{1}{12}s\]
View Solution
8)

For a particle executing SHM the displacement x is given by\[x=A\cos \,\omega t\]. Identify the graph which nrepresents the variation of potential energy (P. E.) as a function of time t and displacement x.

A)
I, III

B)
II, IV

C)
II, III

D)
I, IV
View Solution
9)

The total energy of the particle executing simple harmonic motion of amplitude A is 100 J. At a distance of 0.707 A from the mean position, its kinetic energy is

A)
25J

B)
50J

C)
100J

D)
12.5J
View Solution
10)

When the displacement of a particle executing simple harmonic motion is half of its amplitude, the ratio of its kinetic energy to potential energy

A)
1 : 3

B)
2 : 1

C)
3 : 1

D)
1 : 2
View Solution
11)

The phase difference between the instantaneous velocity and acceleration of a particle executing simple harmonic motion is

A)
\[\pi \]

B)
0.707\[\pi \]

C)
zero

D)
0.5\[\pi \]
View Solution
12)

A particle of mass 1 kg is moving in S.H.M. with an amplitude 0.02 and a frequency of 60 Hz. The maximum force acting on is

A)
144\[{{\pi }^{2}}\]

B)
188 \[{{\pi }^{2}}\]

C)
288\[{{\pi }^{2}}\]

D)
None of these
View Solution
13)

The displacement of a particle in simple harmonic motion in one time period is [A = amplitude]

A)
A

B)
2 A

C)
4 A

D)
Zero
View Solution
14)

Suppose a tunnel is dug along a diameter of the earth. A particle is dropped from a point, a distance h directly above the tunnel, the motion of the particle is

A)
simple harmonic

B)
parabolic

C)
oscillatory

D)
non-periodic
View Solution
15)

The acceleration of a particle undergoing SHM is graphed in figure. At point 2 the velocity of the particle is

A)
zero

B)
negative

C)
positive

D)
None of these
View Solution
16)

A particle starts with S.H.M. from the mean position as shown in figure below. Its amplitude is A and its time period is T. At one time, its speed is half that of the maximum speed. What is the displacement at that time?

A)
\[\frac{\sqrt{2}A}{3}\]

B)
\[\frac{\sqrt{3}A}{2}\]

C)
\[\frac{2A}{\sqrt{3}}\]

D)
\[\frac{3A}{\sqrt{2}}\]
View Solution
17)

A body executing linear simple harmonic motion has a velocity of 3 m/s when its displacement is 4 cm and a velocity of 4 m/s when its displacement is 3 cm. What is the amplitude of oscillation?

A)
5 cm

B)
7.5 cm

C)
10 cm

D)
12.5 cm
View Solution
18)

The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is \[10{{s}^{-1}}\]. At, t = 0 the displacement is 5 m. The initial phase is\[\frac{\pi }{4}\]. What is the maximum acceleration?

A)
\[500m/{{s}^{2}}\]

B)
\[500\,\sqrt{2}\,m/{{s}^{2}}\]

C)
\[750\,\,m/{{s}^{2}}\]

D)
\[750\,\sqrt{2}\,m/{{s}^{2}}\]
View Solution
19)

The displacement of a particle in SHM is\[x=10\sin \left( 2t-\frac{\pi }{6} \right)\] metre. When its displacement is 6 m, the velocity of the particle (in m s~1) is

A)
8

B)
24

C)
16

D)
10
View Solution
20)

Two 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\[{{X}_{0}}({{X}_{0}}>A)\]. If the maximum separation between them is \[({{X}_{0}}+A)\], the phase difference between their motion is

A)
\[\frac{\pi }{3}\]

B)
\[\frac{\pi }{4}\]

C)
\[\frac{\pi }{6}\]

D)
\[\frac{\pi }{2}\]
View Solution
21)

A graph of the square of the velocity against the square of the acceleration of a given simple harmonic motion is

A)

B)

C)

D)

View Solution
22)

For a particle moving according to the equation \[x=a\,\cos \,\pi \,t\], the displacement in 3 s is

A)
0

B)
0.5a

C)
1.5a

D)
2a
View Solution
23)

A body oscillates with SHM according to the equation (in SI units), \[x=5\,\cos \,\left( 2\pi t\frac{\pi }{4} \right)\]. Its instantaneous displacement at t = 1 second is

A)
\[\frac{\sqrt{2}}{5}m\]

B)
\[\frac{1}{\sqrt{3}}m\]

C)
\[\frac{5}{\sqrt{2}}m\]

D)
\[\frac{1}{2}m\]
View Solution
24)

A point mass oscillates along the x-axis according to the law\[x={{x}_{0}}\cos (\omega t-\pi /4)\]. If the acceleration of the particle is written as \[a=A\,\cos (\omega t+\delta )\], then

A)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =3\pi /4\]

B)
\[A={{x}_{0}},\,\delta =-\pi /4\]

C)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =\pi /4\]

D)
\[A={{x}_{0}}{{\omega }^{2}},\,\delta =-\pi /4\]
View Solution
25)

The displacement vs time of a particle executing SHM is shown in figure. The initial phase \[\phi \] is

A)
\[-\pi <\phi <-\frac{\pi }{2}\]

B)
\[\pi <\phi <\frac{3\pi }{2}\]

C)
\[-\frac{3\pi }{2}<\phi <-\pi \]

D)
\[\frac{\pi }{2}<\phi <\pi \]
View Solution
26)

The amplitude of a particle executing SHM is 4 cm. At the mean position the speed of the particle is 16 cm/sec. The distance of the particle from the mean position at which the speed of the particle becomes \[8\sqrt{3}\,cm/s\], will be

A)
\[2\sqrt{3\,}cm\]

B)
\[\sqrt{3\,}cm\]

C)
1cm

D)
2cm
View Solution
27)

Two simple harmonic motions are represented by the equations \[{{y}_{1}}=0.1\sin \left( 100\pi t+\frac{\pi }{3} \right)\]and \[{{y}_{2}}=0.1\cos \pi t\]. The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is

A)
\[\frac{\pi }{3}\]

B)
\[\frac{-\pi }{6}\]

C)
\[\frac{\pi }{6}\]

D)
\[\frac{-\pi }{3}\]
View Solution
28)

Two particles 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

A)
0

B)
\[2\pi /3\]

C)
\[\pi \]

D)
\[\pi /6\]
View Solution
29)

A particle executs SHM with time period 8 s. Initially, it is at its mean position. The ratio of distance travelled by it in the 1st second to that in the 2nd second is

A)
\[\sqrt{2}:1\]

B)
\[1:(\sqrt{2}-1)\]

C)
\[(\sqrt{2}+1):\sqrt{2}\]

D)
\[(\sqrt{2}-1):1\]
View Solution
30)

The x-t graph of a particle undergoing simple harmonic motion is shown below. The acceleration of the particle at t = 4 / 3 s is

A)
\[\frac{\sqrt{3}}{32}{{\pi }^{2}}cm/{{s}^{2}}\]

B)
\[\frac{-{{\pi }^{2}}}{32}cm/{{s}^{2}}\]

C)
\[\frac{{{\pi }^{2}}}{32}cm/{{s}^{2}}\]

D)
\[-\frac{\sqrt{3}}{32}{{\pi }^{2}}cm/{{s}^{2}}\]
View Solution
31)

A particle executing SHM has velocities u and v and acceleration a and b in two of its positions. Find the distance between these two positions.

A)
\[\frac{{{u}^{2}}+{{v}^{2}}}{a+b}\]

B)
\[\frac{{{v}^{2}}+{{u}^{2}}}{a-b}\]

C)
\[\frac{{{v}^{2}}+{{u}^{2}}}{a+b}\]

D)
\[\frac{{{v}^{2}}-{{u}^{2}}}{a-b}\]
View Solution
32)

A particle executing harmonic motion is having velocities \[{{v}_{1}}\] and \[{{v}_{2}}\] at distances is x, and x, from the equilibrium position. The amplitude of the motion is

A)
\[\sqrt{\frac{v_{1}^{2}{{x}_{2}}-v_{2}^{2}{{x}_{1}}}{v_{1}^{2}+v_{2}^{2}}}\]

B)
\[\sqrt{\frac{v_{1}^{2}x_{1}^{2}-v_{2}^{2}x_{2}^{2}}{v_{1}^{2}+v_{2}^{2}}}\]

C)
\[\sqrt{\frac{v_{1}^{2}x_{2}^{2}-v_{2}^{2}x_{1}^{2}}{v_{1}^{2}-v_{2}^{2}}}\]

D)
\[\sqrt{\frac{v_{1}^{2}x_{2}^{2}+v_{2}^{2}x_{1}^{2}}{v_{1}^{2}+v_{2}^{2}}}\]
View Solution
33)

A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency co. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time

A)
at the mean position of the platform

B)
for an amplitude of \[\frac{g}{{{\omega }^{2}}}\]

C)
for an amplitude of\[\frac{g}{{{\omega }^{2}}}\]

D)
at the highest position of the platform
View Solution
34)

Two simple harmonic motions of angular frequency 100 and 1000 r\[rad\,{{s}^{-1}}\]have the same displacement amplitude. The ratio of their maximum accelerations is:

A)
1:10

B)
\[1:{{10}^{2}}\]

C)
\[1:{{10}^{3}}\]

D)
\[1:{{10}^{4}}\]
View Solution
35)

Two particles execute SHM on same straight line with same mean position, same time period 6 second and same amplitude 5cm. Both the particles start SHM from their mean position (in same direction) with a time gap of 1 second. The maximum separation between the two particles during their motion is

A)
2cm

B)
3cm

C)
4cm

D)
5cm
View Solution
36)

A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is\[\frac{1}{4}\], its displacement from its mean position is

A)
\[\frac{2}{\sqrt{5}}A\]

B)
\[\frac{\sqrt{3}}{2}A\]

C)
\[\frac{3}{4}A\]

D)
\[\frac{1}{4}A\]
View Solution
37)

A mass of 4 kg suspended from a spring of force constant 800 N m~1 executes simple harmonic oscillations. If the total energy of the oscillator is 4 J, the maximum acceleration (\[in\,m\,{{s}^{-2}}\]) of the mass is

A)
5

B)
15

C)
45

D)
20
View Solution
38)

A 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 displacement x. Which of the following statement is true?

A)
P.E. is maximum when x = 0.

B)
K.E. is maximum when x = 0.

C)
T. E. is zero when x = 0.

D)
K.E. is maximum when x is maximum.
View Solution
39)

If< E > and denote the average kinetic and the average potential energies respectively of mass describing a simple harmonic motion, over one period, then the correct relation is

A)
<E>=

B)
<E>=2

C)
<E>=-2

D)
<E>=-
View Solution
40)

What do you conclude from the graph about the frequency of KE, PE and SHM?

A)
Frequency of KE and PE is double the frequency of SHM.

B)
Frequency of KE and PE is four times the frequency SHM.

C)
Frequency of PE is double the frequency of K.E.

D)
Frequency of KE and PE is equal to the frequency of SHM.
View Solution
41)

A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is

A)
\[2{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\]

B)
       \[{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\]

C)
\[\frac{1}{4}m{{a}^{2}}{{v}^{2}}\]

D)
       \[4{{\pi }^{2}}m{{a}^{2}}{{v}^{2}}\]
View Solution
42)

A particle of mass m is executing oscillations about the origin on the X-axis with amplitude A. Its potential energy is given as \[U(x)=\alpha {{x}^{4}}\] where a is a positive constant. The x coordinate of the particle where the potential energy is one third of the kinetic energy is

A)
\[\pm A/2\]

B)
\[\pm A/\sqrt{2}\]

C)
\[\pm A/3\]

D)
\[\pm A/\sqrt{3}\]
View Solution
43)

A particle of mass 10 gm is describing S.H. M. along a straight line with period of 2 sec and amplitude of 10 cm. Its kinetic energy when it is at 5 cm from its equilibrium position is

A)
\[37.5{{\pi }^{2}}\,ergs\]

B)
\[3.75{{\pi }^{2}}\,ergs\]

C)
\[375{{\pi }^{2}}\,ergs\]

D)
\[0.375{{\pi }^{2}}\,erg\]
View Solution
44)

A particle of mass 1 kg is placed in a potential field. Its potential energy is given by \[U=10{{x}^{2}}+5\].The frequency of oscillations of the particle is given by

A)
\[(\sqrt{10})\]

B)
\[(\sqrt{5})\]

C)
\[\left( \sqrt{\frac{10}{\pi }} \right)\]

D)
\[\left( \frac{\sqrt{5}}{\pi } \right)\]
View Solution
45)

A body is executing simple harmonic motion. At a displacement x from mean position, its potential energy is \[{{E}_{1}}=2J\] and at a displacement y from mean position, its potential energy is\[{{E}_{2}}=8J\]. The potential energy E at a displacement (x + y) from mean position is

A)
10J

B)
14J

C)
18J

D)
4J
View Solution
46)

The particle executing simple harmonic motion has a kinetic energy\[{{K}_{0}}{{\cos }^{2}}\omega t\]. The maximum values of the potential energy and the total energy are respectively

A)
\[{{K}_{0}}/2\,and\,{{K}_{0}}\]

B)
       \[{{K}_{0}}\,and\,2{{K}_{0}}\]

C)
\[{{K}_{0}}\,and\,{{K}_{0}}\]

D)
       \[0\,and\,2{{K}_{0}}\]
View Solution
47)

A particle of mass m oscillates with simple harmonic motion between points \[{{x}_{1}}\] and \[{{x}_{2}}\], the equilibrium position being O. Its potential energy is plotted. It will be as given below in the graph.

A)

B)

C)

D)

View Solution
48)

A linear harmonic oscillator of force constant \[2\times {{10}^{6}}N/m\] and amplitude 0.01 m has a total mechanical energy of 160 J. Its

A)
potential energy is 160 J

B)
potential energy is 100 J

C)
potential energy is zero

D)
potential energy is 120 J
View Solution
49)

The angular velocity and the amplitude of a simple pendulum is o and a respectively. At a displacement x from the mean position if its kinetic energy is T and potential energy is V, then the ratio of T to Vis

A)
\[\frac{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}{{{x}^{2}}{{\omega }^{2}}}\]

B)
\[\frac{{{x}^{2}}{{\omega }^{2}}}{({{a}^{2}}-{{x}^{2}}{{\omega }^{2}})}\]

C)
\[\frac{({{a}^{2}}-{{x}^{2}})}{{{x}^{2}}}\]

D)
\[\frac{{{x}^{2}}}{({{a}^{2}}-{{x}^{2}})}\]
View Solution
50)

A simple pendulum oscillates in air with time period T and amplitude A. As the time passes

A)
T and A both decrease

B)
T increases and A is constant

C)
T remains same and A decreases

D)
T decreases and A is constant
View Solution
51)

If the maximum velocity and acceleration of a particle executing SHM are equal in magnitude, the time period will be

A)
1.57 sec

B)
3.14 sec

C)
6.28 sec

D)
12.56 sec
View Solution
52)

A particle executes simple harmonic motion between \[x=-A\] and \[x=+A\]. The time taken for it to go from O to A/2 is \[{{T}_{1}}\] and\[{{T}_{1}}\] and to go from A/2 to A is \[{{T}_{2}}\]. Then

A)
\[{{T}_{1}}<{{T}_{2}}\]

B)
\[{{T}_{1}}>{{T}_{2}}\]

C)
\[{{T}_{1}}={{T}_{2}}\]

D)
\[{{T}_{1}}=2{{T}_{2}}\]
View Solution
53)

If a particle takes 0.5 sec to reach position of minimum velocity from previous such position, then

A)
\[T=6\sec ,\,v=1/6\,Hz\]

B)
\[T=2\sec ,\,v=1\,Hz\]

C)
\[T=3\sec ,\,v=3\,Hz\]

D)
\[T=1\sec ,\,v=1\,Hz\]
View Solution
54)

A simple harmonic motion has an amplitude A and time period T. The time required by it to travel from x=A to x=A/2 is

A)
T/6

B)
T/4

C)
T/3

D)
T/2
View Solution
55)

Frequency of oscillation is proportional to

A)
\[\sqrt{\frac{3k}{m}}\]

B)
\[\sqrt{\frac{k}{m}}\]

C)
\[\sqrt{\frac{2k}{m}}\]

D)
\[\sqrt{\frac{m}{3k}}\]
View Solution
56)

The bob of a simple pendulum of mass m and total energy E will have maximum linear momentum equal to

A)
\[\sqrt{\frac{2E}{m}}\]

B)
\[\sqrt{2mE}\]

C)
\[2mE\]

D)
\[m{{E}^{2}}\]
View Solution
57)

A particle executing simple harmonic motion covers a distance equal to half of its amplitude in one second. Then the time period of the simple harmonic motion is

A)
4s

B)
6s

C)
8s

D)
12s
View Solution
58)

The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm, is 4.4 m/s. The period of oscillation is

A)
0.01s

B)
10s

C)
0.ls

D)
100s
View Solution
59)

A body is executing S.H.M. When its displacement from the mean position are 4 cm and 5 cm, it has velocities \[10cm\,{{s}^{-1}}\] and \[8\,cm\,{{s}^{-1}}\] respectively. Its periodic time is

A)
\[\pi /2\,s\]

B)
\[\pi s\]

C)
\[3\pi /2s\]

D)
\[2\pi s\]
View Solution
60)

The displacement of an object "attached to a spring and executing simple harmonic motion is given by \[x=2\times {{10}^{-2\,\,\,}}\cos \,\pi t\] metre. The time at which the maximum speed first occurs is

A)
0.25s

B)
0.5s

C)
0.75s

D)
0.125s
View Solution
61)

A particle at the end of a spring executes S.H.M with a period\[{{t}_{1}}\], while the corresponding period for another spring is \[{{t}_{2}}\]. If the period of oscillation with the two springs in series is T then

A)
\[{{T}^{-1}}={{t}_{1}}^{-1}+{{t}_{2}}^{-1}\]

B)
\[{{T}^{2}}=t_{1}^{2}+t_{2}^{2}\]

C)
\[T={{t}_{1}}+{{t}_{2}}\]

D)
\[{{T}^{-2}}=t_{1}^{-2}+t_{2}^{-2}\]
View Solution
62)

A 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)
\[2\pi \sqrt{\frac{x_{2}^{2}-x_{1}^{2}}{V_{1}^{2}-V_{2}^{2}}}\]

B)
\[2\pi \sqrt{\frac{V_{1}^{2}+V_{2}^{2}}{x_{1}^{2}+x_{2}^{2}}}\]

C)
\[2\pi \sqrt{\frac{V_{1}^{2}-V_{2}^{2}}{x_{1}^{2}-x_{2}^{2}}}\]

D)
\[2\pi \sqrt{\frac{x_{1}^{2}-x_{2}^{2}}{V_{1}^{2}-V_{2}^{2}}}\]
View Solution
63)

A simple harmonic wave having an amplitude a and time period T is represented by the equation\[y=5\sin \pi (t+4)m\]. Then the value of amplitude in (m) and time period (T) in second are

A)
\[a=10,\,T=2\]

B)
       a=5,T=l

C)
a=10,T=l

D)
a=5,T=2
View Solution
64)

What will be the force constant of the spring system shown in figure?

A)
\[\frac{{{k}_{1}}}{2}+{{k}_{2}}\]

B)
\[{{\left[ \frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]}^{-1}}\]

C)
\[\left[ \frac{1}{2{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]\]

D)
\[{{\left[ \frac{2}{{{k}_{1}}}+\frac{1}{{{k}_{2}}} \right]}^{-1}}\]
View Solution
65)

A particle of mass m oscillates with a potential energy\[U={{U}_{0}}+\alpha \,\,{{x}^{2}}\], where \[{{U}_{0}}\] and a are constants and x is the displacement of particle from equilibrium position. The time period of oscillation is

A)
\[2\pi \sqrt{\frac{m}{\alpha }}\]

B)
\[2\pi \sqrt{\frac{m}{2\alpha }}\]

C)
\[\pi \sqrt{\frac{2m}{\alpha }}\]

D)
\[2\pi \sqrt{\frac{m}{{{\alpha }^{2}}}}\]
View Solution
66)

The average value of potential energy for one complete oscillation cycle of a body of mass m executing S.H.M. having angular frequency \[\omega \] and maximum amplitude a is given by:

A)
\[\frac{1}{2}m{{\omega }^{2}}{{a}^{2}}\]

B)
\[\frac{1}{4}m{{\omega }^{2}}{{a}^{2}}\]

C)
\[\frac{1}{8}m{{\omega }^{2}}{{a}^{2}}\]

D)
\[\frac{1}{16}m{{\omega }^{2}}{{a}^{2}}\]
View Solution
67)

A wall clock uses a vertical spring-mass system to measure the time. Each time the mass reaches an extreme position, the clock advances by a second. The clock gives correct time at the equator. If the clock is taken to the poles it will

A)
run slow

B)
run fast

C)
stop working

D)
give correct time
View Solution
68)

The height of liquid column in a U tube is 0.3 m. If the liquid in one of the limbs is depressed and then released, then the time period of the liquid column will be

A)
1.1 sec

B)
19 sec

C)
0.11 sec

D)
2 sec
View Solution
69)

A block rests on a horizontal table which is executing SHM in the horizontal plane with an amplitude 'a'. If the coefficient of friction is \['\mu '\], then the block just starts to slip when the frequency of oscillation is

A)
\[\frac{1}{2\pi }\sqrt{\frac{\mu g}{a}}\]

B)
\[\sqrt{\frac{\mu g}{a}}\]

C)
\[2\pi \sqrt{\frac{a}{\mu g}}\]

D)
\[\sqrt{\frac{a}{\mu g}}\]
View Solution
70)

On earth, a body suspended on a spring of negligible mass causes extension L and undergoes oscillations along length of the spring with frequency f. On the Moon, the same quantities are L/n and f respectively. The ratio f?/f is

A)
n

B)
\[\frac{1}{n}\]

C)
\[{{n}^{-1/2}}\]

D)
1
View Solution
71)

A second's pendulum is placed in a space laboratory orbiting around the earth at a height 3 R from the earth's surface where R is earth's radius. The time period of the pendulum will be

A)
zero

B)
\[2\sqrt{3}\]

C)
4 sec

D)
infinite
View Solution
72)

A bent tube of uniform cross-section area A has a non-viscous liquid of density p. The mass of liquid in the tube is m. The time period of oscillation of the liquid is

A)
\[2\pi \sqrt{\frac{m}{\rho gA}}\]

B)
\[2\pi \sqrt{\frac{m}{2\rho gA}}\]

C)
\[2\pi \sqrt{\frac{2m}{\rho gA}}\]

D)
None of these
View Solution
73)

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to\[{{T}_{M}}\]. If the Young's modulus of the material of the wire is Y then\[\frac{1}{Y}\] is equal to: (g = gravitational acceleration)

A)
\[\left[ 1-{{\left( \frac{{{T}_{M}}}{T} \right)}^{2}} \right]\frac{A}{Mg}\]

B)
       \[\left[ 1-{{\left( \frac{T}{{{T}_{M}}} \right)}^{2}} \right]\frac{A}{Mg}\]

C)
\[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{A}{Mg}\]

D)
       \[\left[ {{\left( \frac{{{T}_{M}}}{T} \right)}^{2}}-1 \right]\frac{Mg}{A}\]
View Solution
74)

Masses \[{{M}_{A}}\] and \[{{M}_{B}}\] hanging from the ends of strings of lengths \[{{L}_{A}}\] and \[{{L}_{B}}\] are executing simple harmonic- motions. If their frequencies are \[{{f}_{A}}=2{{f}_{B}}\], then

A)
\[{{L}_{A}}=2{{L}_{B}}\,and\,{{M}_{A}}={{M}_{B}}/2\]

B)
\[{{L}_{A}}=4{{L}_{B}}\] regardless of masses

C)
\[{{L}_{A}}={{L}_{B}}/4\] regardless of masses

D)
\[{{L}_{A}}=2{{L}_{B}}\,\,\,and\,{{M}_{A}}=2{{M}_{B}}\]
View Solution
75)

A simple pendulum has time period\[{{T}_{1}}\]. The point of suspension is now moved upward according to the relation \[y=K{{t}^{2}},(K=1m/{{s}^{2}})\] where y is the vertical displacement. The time period now becomes\[{{T}_{2}}\]. The ratio of \[\frac{T_{1}^{2}}{T_{2}^{2}}\] is \[(g=10m/{{s}^{2}})\]

A)
5/6

B)
6/5

C)
1

D)
4/5
View Solution
76)

A cylindrical block of wood (density = 650 kg \[{{m}^{-3}}\]), of base area 30cm2 and height 54 cm, floats in a liquid of density 900 kg \[{{m}^{-3}}\]. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly)

A)
52cm

B)
65cm

C)
39cm

D)
26cm
View Solution
77)

A body executes simple harmonic motion under the action of a force \[{{F}_{1}}\] with a time period \[\frac{4}{5}\]s. If the force is changed to\[{{F}_{2}}\], it executes S.H.M. with time period - s. If both the forces \[{{F}_{1}}\] and \[{{F}_{2}}\] act simultaneously in the same direction on the body, its time period in second is

A)
\[\frac{12}{25}\]

B)
\[\frac{7}{5}\]

C)
\[\frac{24}{25}\]

D)
\[\frac{5}{7}\]
View Solution
78)

If the differential equation for a simple harmonic motion is \[\frac{{{d}^{2}}{{y}^{2}}}{d{{t}^{2}}}+2y=0\], the time-period of the motion is

A)
\[\pi \sqrt{2}s\]

B)
\[\frac{\sqrt{2}s}{\pi }\]

C)
\[\frac{\pi }{\sqrt{2}}\]

D)
\[2\pi s\]
View Solution
79)

Four massless springs whose force constants are 2k, 2k, k and 2k respectively are attached to a mass M kept on a frictionless plane (as shown in figure). If the mass M is displaced in the horizontal direction, then the frequency of the system is

A)
\[\frac{1}{2\pi }\sqrt{\frac{k}{4M}}\]

B)
\[\frac{1}{2\pi }\sqrt{\frac{4k}{M}}\]

C)
\[\frac{1}{2\pi }\sqrt{\frac{k}{7M}}\]

D)
\[\frac{1}{2\pi }\sqrt{\frac{7k}{M}}\]
View Solution
80)

The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is \[{{t}_{0}}\]in air. Neglecting frictional force of water and given that the density of the bob is\[(4/3)\times 1000kg/{{m}^{3}}\]. What relationship between t and \[{{t}_{0}}\] is true?

A)
\[t={{t}_{0}}\]

B)
\[t={{t}_{0}}/2\]

C)
\[t=2{{t}_{0}}\]

D)
\[t=4{{t}_{0}}\]
View Solution
81)

A U-tube is of non uniform cross-section. The area of cross-sections of two sides of tube are A and 2A (see fig.). It contains non-viscous liquid of mass m. The liquid is displaced slightly and free to oscillate. Its time period of oscillations is

A)
\[T=2\pi \sqrt{\frac{m}{3\rho gA}}\]

B)
\[T=2\pi \sqrt{\frac{m}{2\rho gA}}\]

C)
\[T=2\pi \sqrt{\frac{m}{\rho gA}}\]

D)
None of these
View Solution
82)

A small ball of density \[4{{\rho }_{0}}\] is released from rest just below the surface of a liquid. The density of liquid increases with depth as \[\rho ={{\rho }_{0}}(1+ay)\] where \[a=2{{m}^{-1}}\]is a constant. Find the time period of its oscillation. (Neglect the viscosity effects).

A)
\[\frac{2\pi }{\sqrt{5}}\sec \]

B)
\[\frac{\pi }{\sqrt{5}}\sec \]

C)
\[\frac{\pi }{2\sqrt{5}}\sec \]

D)
\[\frac{3\pi }{2\sqrt{5}}\sec \]
View Solution
83)

A rod of mass M and length L is hinged at its centre of mass so that it can rotate in a vertical plane. Two springs each of stiffness k are connected at its ends, as shown in the figure. The time period of SHM is

A)
\[2\pi \sqrt{\frac{M}{6k}}\]

B)
\[2\pi \sqrt{\frac{M}{3k}}\]

C)
\[2\pi \sqrt{\frac{ML}{k}}\]

D)
\[\pi \sqrt{\frac{M}{6k}}\]
View Solution
84)

Disregarding gravity, find the period of oscillation of the particle connected with four springs as shown in the figure. (Given:\[\theta ={{45}^{o}},\beta ={{30}^{o}}\])

A)
\[\pi \sqrt{\frac{2m}{k}}\]

B)
\[\sqrt{\frac{2m\pi }{k}}\]

C)
\[\sqrt{\frac{m\pi }{2k}}\]

D)
\[\pi \sqrt{\frac{m}{2k}}\]
View Solution
85)

Two springs, each of spring constant\[k=100N/m\], are attached to a block of mass 2 kg as shown in the figure. The block can slide smoothly along a horizontal platform clamped to the opposite walls of the trolley of mass 5kg. If the block is displaced by x cm. and released, the period of oscillation in seconds is

A)
\[T=2\pi \sqrt{\frac{1}{20}}\]

B)
\[T=2\pi \sqrt{\frac{7}{1000}}\]

C)
\[T=2\pi \sqrt{\frac{1}{140}}\]

D)
\[T=2\pi \frac{49}{100}\]
View Solution
86)

If a body oscillates at the angular frequency \[{{\omega }_{d}}\] of the driving force, then the oscillations are called

A)
free oscillations

B)
coupled oscillations

C)
forced oscillations

D)
maintained oscillations
View Solution
87)

In case of a forced vibration, the resonance wave becomes very sharp when the

A)
quality factor is small

B)
damping force is small

C)
restoring force is small

D)
applied periodic force is small
View Solution
88)

When an oscillator completes 100 oscillations its amplitude reduces to\[\frac{1}{3}\] of its initial value. What will be its amplitude, when it complete 200 oscillations?

A)
\[\frac{1}{8}\]

B)
\[\frac{2}{3}\]

C)
     \[\frac{1}{6}\]

D)
\[\frac{1}{9}\]
View Solution
89)

A forced oscillator is acted upon by a force \[F={{F}_{0}}\] sin cot. The amplitude of oscillation is given by \[\frac{55}{\sqrt{2{{\omega }^{2}}-36\omega +9}}\]. The resonant angular frequency is

A)
2 unit

B)
9 unit

C)
18 unit

D)
36 unit
View Solution
90)

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force F sin\[\omega t\]. 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

A)
\[{{\omega }_{1}}={{\omega }_{2}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\]

B)
\[{{\omega }_{1}}={{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\]

C)
\[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}={{\omega }_{0}}\]

D)
\[{{\omega }_{1}}\ne {{\omega }_{0}}\,and\,{{\omega }_{2}}\ne {{\omega }_{0}}\]
View Solution
91)

A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency\[{{\omega }_{0}}\]. An external force F (t) proportional to \[\cos \,\omega t(\omega \ne {{\omega }_{0}})\] is applied to the oscillator. The displacement of the oscillator will be proportional to

A)
\[\frac{1}{m(\omega _{0}^{2}+{{\omega }^{2}})}\]

B)
\[\frac{1}{m(\omega _{0}^{2}-{{\omega }^{2}})}\]

C)
\[\frac{m}{\omega _{0}^{2}-{{\omega }^{2}}}\]

D)
\[\frac{m}{(\omega _{0}^{2}+{{\omega }^{2}})}\]
View Solution
92)

What is the amplitude of simple harmonic motion at resonance in the ideal case of zero damping?

A)
Zero

B)
-1

C)
1

D)
Infinite
View Solution
93)

If a simple pendulum has significant amplitude (upto a factor of \[1/e\] of original) only in the period between \[t=0s\,to\,t=\tau s\], 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 of proportionality, the average life time of the pendulum is (assuming damping the small) in seconds

A)
\[\frac{0.693}{b}\]

B)
b

C)
\[\frac{1}{b}\]

D)
\[\frac{2}{b}\]
View Solution
94)

A pendulum with time period of 1s is losing energy. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s~1) is :

A)
\[\frac{1}{2}\]

B)
\[\frac{1}{30}\]

C)
2

D)
\[\frac{1}{15}In\,3\]
View Solution
95)

In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value \[{{a}_{0}}\] at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

A)
\[{{a}_{0}}/2\]

B)
\[{{a}_{0}}/4\]

C)
\[{{a}_{0}}/6\]

D)
\[{{a}_{0}}/9\]
View Solution
96)

A block connected to a spring oscillates vertically. A damping force\[{{F}_{d}}\] , acts on the block by the surrounding medium. Given as \[{{F}_{d}}=-bVb\] is a positive constant which depends on :

A)
viscosity of the medium

B)
size of the block

C)
shape of the block

D)
All of these
View Solution
97)

The amplitude of a damped oscillator becomes\[{{\left( \frac{1}{3} \right)}^{rd}}\] in 2 seconds. If its amplitude after 6 seconds is\[\frac{1}{n}\] times the original amplitude, the value of n is

A)
\[{{3}^{2}}\]

B)
\[{{3}^{3}}\]

C)
\[\sqrt[3]{3}\]

D)
\[{{2}^{3}}\]
View Solution
98)

In case of sustained forced oscillations the amplitude of oscillations

A)
decreases linearly

B)
decreases sinusoidally

C)
decreases exponentially

D)
always remains constant
View Solution
99)

The amplitude of velocity of a particle is given by, \[{{V}_{m}}={{V}_{0}}/(a{{\omega }^{2}}-b\omega +c)\] where \[{{V}_{0}}\], a, b and c are positive: The condition for a single resonant frequency is

A)
\[{{b}^{2}}<4ac\]

B)
\[{{b}^{2}}=4ac\]

C)
\[{{b}^{2}}=5ac\]

D)
\[{{b}^{2}}=7ac\]
View Solution
100)

The time period of simple pendulum of length 1m suspended in a car that is moving with constant speed 36 km/hr around a circle of radius 10mis:

A)
\[\pi \sqrt{2}\sec \]

B)
\[\frac{\pi }{10}\sqrt{2}\sec \]

C)
\[\frac{\pi }{10\sqrt{2}}\sec \]

D)
\[\frac{5\pi }{\sqrt{2}}\sec \]
View Solution

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Self Evaluation Test - Oscillations

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JEE Main & Advanced Physics Wave Mechanics Question Bank

done Self Evaluation Test - Oscillations Total Questions - 100

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Self Evaluation Test - Oscillations

Self Evaluation Test - Oscillations Total Questions - 100