# 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.

Physics
Chemistry
Maths

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}