JEE Main > Oscillations and Waves

Explore popular questions from Oscillations and Waves for JEE Main. This collection covers Oscillations and Waves previous year JEE Main questions hand picked by popular teachers.


Q 1.    

Correct4

Incorrect-1

In a simple harmonic oscillator, at the mean position

A

kinetic energy is minimum, potential energy is maximum

B

both kinetic and potential energies are maximum

kinetic energy is maximum, potential energy is minimum

D

both kinetic and potential energies are minimum.

Explanation

Q 2.    

Correct4

Incorrect-1

If a spring has time period {tex} \mathrm { T } , {/tex} and is cut into {tex} n {/tex} equal parts, then the time period of each part will be

A

{tex} T \sqrt { n } {/tex}

{tex} T / \sqrt { n } {/tex}

C

{tex} n T {/tex}

D

{tex} T {/tex}

Explanation

Q 3.    

Correct4

Incorrect-1

A child swinging on a swing in sitting position, stands up, then the time period of the swing will

A

increase

decrease

C

remains same

D

increases of the child is long and decreases if the child is short

Explanation



Q 4.    

Correct4

Incorrect-1

A mass {tex} M {/tex} is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period {tex} T . {/tex} If the mass is increased by {tex} \mathrm { m } , {/tex} the time period becomes {tex} \frac { 5 T } { 3 } . {/tex} Then the ratio of {tex} \frac { m } { M } {/tex} is

A

{tex} \frac { 3 } { 5 } {/tex}

B

{tex} \frac { 25 } { 9 } {/tex}

{tex} \frac { 16 } { 9 } {/tex}

D

{tex} \frac { 5 } { 3 } {/tex}

Explanation



Q 5.    

Correct4

Incorrect-1

Two particles {tex} A {/tex} and {tex} B {/tex} of equal masses are suspended from two massless springs of spring of spring constant {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } , {/tex} respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of {tex} A {/tex} and {tex} B {/tex} is

A

{tex} \sqrt { \frac { k _ { 1 } } { k _ { 2 } } } {/tex}

B

{tex} \frac { k _ { 2 } } { k _ { 1 } } {/tex}

{tex} \sqrt { \frac { k _ { 2 } } { k _ { 1 } } } {/tex}

D

{tex} \frac { k _ { 1 } } { k _ { 2 } } {/tex}

Explanation



Q 6.    

Correct4

Incorrect-1

The length of a simple pendulum executing simple harmonic motion is increased by 21{tex} \% {/tex} . The percentage increase in the time period of the pendulum of increased length is {tex} {/tex}

A

11{tex} \% {/tex}

B

21{tex} \% {/tex}

C

42{tex} \% {/tex}

10{tex} \% {/tex}

Explanation



Q 7.    

Correct4

Incorrect-1

The displacement of a particle varies according to the relation {tex} x = 4 ( \cos \pi t + \sin \pi t ) . {/tex} The amplitude of the particle is

A

{tex} - 4 {/tex}

B

4

4{tex} \sqrt { 2 } {/tex}

D

8

Explanation

Q 8.    

Correct4

Incorrect-1

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 {tex} x {/tex} . Which of the following statements is true?

K.E. is maximum when {tex} x = 0 {/tex}

B

T.E is zero when {tex} x = 0 {/tex}

C

K.E is maximum when {tex} x {/tex} is maximum

D

P.E is maximum when {tex} x = 0 {/tex}

Explanation

Q 9.    

Correct4

Incorrect-1

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

{tex} t = 2 t _ { 0 } {/tex}

B

{tex} t = t _ { 0 } / 2 {/tex}

C

{tex} t = t _ { 0 } {/tex}

D

{tex} t = 4 t _ { 0 } {/tex}

Explanation







Q 10.    

Correct4

Incorrect-1

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

A

{tex} T ^ { - 1 } = t _ { 1 } ^ { - 1 } + t _ { 2 } ^ { - 1 } {/tex}

{tex} T ^ { 2 } = t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 } {/tex}

C

{tex} T = t _ { 1 } + t _ { 2 } {/tex}

D

{tex} T ^ { - 2 } = t _ { 1 } ^ { - 2 } + t _ { 2 } ^ { - 2 } {/tex}

Explanation





Q 11.    

Correct4

Incorrect-1

The total energy of a particle, executing simple harmonic motion is

independent of {tex} x {/tex}

B

{tex} \propto x ^ { 2 } {/tex}

C

{tex} \propto x {/tex}

D

{tex} \propto x ^ { 1 / 2 } {/tex}

Explanation

Q 12.    

Correct4

Incorrect-1

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

A

{tex} \frac { 1 } { m \left( \omega _ { 0 } ^ { 2 } + \omega ^ { 2 } \right) } {/tex}

{tex} \frac { 1 } { m \left( \omega _ { 0 } ^ { 2 } - \omega ^ { 2 } \right) } {/tex}

C

{tex} \frac { m } { \omega _ { 0 } ^ { 2 } - \omega ^ { 2 } } {/tex}

D

{tex} \frac { m } { \left( \omega _ { 0 } ^ { 2 } + \omega ^ { 2 } \right) } {/tex}

Explanation

Q 13.    

Correct4

Incorrect-1

In forced oscillation of a particle the amplitude is maximum for a frequency {tex} \omega _ { 1 } {/tex} of the force while the energy is maximum for a frequencyo, of the force; then

A

{tex} \omega _ { 1 } < \omega _ { 2 } {/tex} when damping is small and {tex} \omega _ { 1 } > \omega _ { 2 } {/tex} when damping is large

B

{tex} \omega _ { 1 } > \omega _ { 2 } {/tex}

{tex} \omega _ { 1 } = \omega _ { 2 } {/tex}

D

{tex} \omega _ { 1 } < \omega _ { 2 } {/tex}

Explanation



Q 14.    

Correct4

Incorrect-1

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

A

{tex} \frac { \pi } { 3 } {/tex}

{tex} \frac { - \pi } { 6 } {/tex}

C

{tex} \frac { \pi } { 6 } {/tex}

D

{tex} \frac { - \pi } { 3 } {/tex}

Explanation



Q 15.    

Correct4

Incorrect-1

The function {tex} \sin ^ { 2 } ( \omega t ) {/tex} represents

A

a periodic, but not SHM with a period {tex} \frac { \pi } { \omega } {/tex}

B

a periodic, but not SHM with a period {tex} \frac { 2 \pi } { \omega } {/tex}

a SHM with a period {tex} \frac { \pi } { \omega } {/tex}

D

a SHM with a period {tex} \frac { 2 \pi } { \omega } {/tex}

Explanation

Q 16.    

Correct4

Incorrect-1

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

A

first decrease and then increase to the original value

first increase and then decrease to the original value

C

increase towards a saturation value

D

remain unchanged

Explanation





Q 17.    

Correct4

Incorrect-1

If a simple harmonic motion is represented by {tex} \frac { d ^ { 2 } x } { d t ^ { 2 } } + \alpha x = 0 , {/tex} its time period is

{tex} \frac { 2 \pi } { \sqrt { \alpha } } {/tex}

B

{tex} \frac { 2 \pi } { \alpha } {/tex}

C

2{tex} \pi \sqrt { \alpha } {/tex}

D

2{tex} \pi \alpha {/tex}

Explanation



Q 18.    

Correct4

Incorrect-1

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

{tex}0.01\, \mathrm { s } {/tex}

B

{tex}10\, s {/tex}

C

{tex}0.1\, \mathrm { s } {/tex}

D

100{tex} \mathrm { s } {/tex}

Explanation



Q 19.    

Correct4

Incorrect-1

Starting from the origin a body oscillates simple harmonically with a period of {tex} 2s {/tex}. After what time will its kinetic energy be {tex} 75 \% {/tex} of the total energy?

{tex} \frac{1}{6}s {/tex}

B

{tex} \frac{1}{4}s {/tex}

C

{tex} \frac{1}{3}s {/tex}

D

{tex} \frac{1}{12}s {/tex}

Explanation



Q 20.    

Correct4

Incorrect-1

Two springs, of force constants {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } {/tex} are connected to a mass {tex} m {/tex} as shown. The frequency of oscillation of the mass is {tex} f {/tex} . If both {tex} k _ { 1 } {/tex} and {tex} k _ { 2 } {/tex} are made four times their original values, the frequency of oscillation becomes

2{tex} f {/tex}

B

{tex} f / 2 {/tex}

C

{tex} f / 4 {/tex}

D

4{tex} f {/tex}

Explanation



Q 21.    

Correct4

Incorrect-1

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

A

2{tex} \pi ^ { 2 } m a ^ { 2 } v ^ { 2 } {/tex}

{tex} \pi ^ { 2 } m a ^ { 2 } v ^ { 2 } {/tex}

C

{tex} \frac { 1 } { 4 } m a ^ { 2 } v ^ { 2 } {/tex}

D

4{tex} \pi ^ { 2 } m a ^ { 2 } v ^ { 2 } {/tex}

Explanation

Q 22.    

Correct4

Incorrect-1

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

A

0.25{tex} \mathrm { s } {/tex}

0.5{tex} \mathrm { s } {/tex}

C

0.75{tex} \mathrm { s } {/tex}

D

0.125{tex} \mathrm { s } {/tex}

Explanation



Q 23.    

Correct4

Incorrect-1

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

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

B

{tex} A = x _ { 0 } , \delta = - \pi / 4 {/tex}

C

{tex} A = x _ { 0 } \omega ^ { 2 } , \delta = \pi / 4 {/tex}

D

{tex} A = x _ { 0 } \omega ^ { 2 } , \delta = - \pi / 4 {/tex}

Explanation







Q 24.    

Correct4

Incorrect-1

If {tex} x , v {/tex} and {tex} a {/tex} denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period {tex} T , {/tex} then, which of the following does not change with time?

{tex} a T / x {/tex}

B

{tex} a T + 2 \pi v {/tex}

C

{tex} a T / v {/tex}

D

{tex} a ^ { 2 } T ^ { 2 } + 4 \pi ^ { 2 } v ^ { 2 } {/tex}

Explanation

Q 25.    

Correct4

Incorrect-1

Two particles are executing simple harmonic motion of the same amplitude {tex} A {/tex} and frequency {tex} \omega {/tex} along the {tex} x {/tex} -axis. Their mean position is separated by distance {tex} X _ { 0 } \left( X _ { 0 } > A \right) . {/tex} If the maximum separation between them is {tex} \left( X _ { 0 } + A \right) , {/tex} the phase difference between their motion is:

A

{tex} \frac { \pi } { 3 } {/tex}

B

{tex} \frac { \pi } { 4 } {/tex}

C

{tex} \frac { \pi } { 6 } {/tex}

{tex} \frac { \pi } { 2 } {/tex}

Explanation