# NEET

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

## Biology

Oscillations and Waves

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Q 1. A particle of mass m executes simple harmonic motion with amplitude {tex} a {/tex} and frequency {tex} v {/tex} . The average kinetic energy {tex} y {/tex} 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 } y ^ { 2 } {/tex}

##### Explanation

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

A

{tex} 3 ^ { 2 } {/tex}

{tex} 3 ^ { 3 } {/tex}

C

{tex} \sqrt [ 3 ] { 3 } {/tex}

D

{tex} 2 ^ { 3 } {/tex}

##### Explanation

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Q 3. Assume the earth to be perfect sphere of uniform density. If a body is dropped at one end of a tunnel dug along a diameter of the earth (remember that inside the tunnel the force on the body is -k times the displacement from the centre, k being a constant), it (body) will

A

reach the earth's centre and stay there

B

go through the tunnel and comes out at the other end

oscillate simple harmonically in the tunnel

D

stay somewhere between the earth's centre and one of the ends of tunnel.

##### Explanation

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Q 4. A particle undergoes simple harmonic motion having time period T. The time taken in {tex}3 / 8 {/tex} th oscillation is

A

{tex} \frac { 3 } { 8 } \mathrm { T } {/tex}

B

{tex} \frac { 5 } { 8 } \mathrm { T } {/tex}

{tex} \frac { 5 } { 12 } \mathrm { T } {/tex}

D

{tex} \frac { 7 } { 12 } \mathrm { T } {/tex}

##### Explanation

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Q 5. A particle is executing simple harmonic motion with amplitude A. When the ratio of its kinetic energy to the potential energy is {tex} \frac { 1 } { 4 } , {/tex} its displacement from its mean position is

{tex} \frac { 2 } { \sqrt { 5 } } \mathrm { A } {/tex}

B

{tex} \frac { \sqrt { 3 } } { 2 } \mathrm { A } {/tex}

C

{tex} \frac { 3 } { 4 } \mathrm { A } {/tex}

D

{tex} \frac { 1 } { 4 } \mathrm { A } {/tex}

##### Explanation

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Q 6. 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

A

1{tex} \% {/tex}

B

21{tex} \% {/tex}

C

42{tex} \% {/tex}

10{tex} \% {/tex}

##### Explanation

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Q 7. The time period of a mass suspended from a spring is {tex} T . {/tex} If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be

A

2{tex} T {/tex}

B

{tex} \frac { T } { 4 } {/tex}

C

2

{tex} \frac { T } { 2 } {/tex}

##### Explanation

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Q 8. Two simple harmonic motions act on a particle. These harmonic motions are {tex} x = A \cos ( \omega t + \delta ) , y = A \cos ( \omega t + \alpha ) {/tex} when {tex} \delta = \alpha + \frac { \pi } { 2 } , {/tex} the resulting motion is

A

a circle and the actual motion is clockwise

B

an ellipse and the actual motion is counterclockwise

C

an elllipse and the actual motion is clockwise

a circle and the actual motion is counter clockwise

##### Explanation

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Q 9. A point mass oscillates along the {tex} x {/tex} -axis according to the law {tex} x = x _ { 0 } \cos ( \omega t - \pi / 4 ) . {/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

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Q 10. 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}

A

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

B

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

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

D

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

##### Explanation

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Q 11. A body oscillates with a simple harmonic motion having amplitude 0.05{tex} \mathrm { m } {/tex} . At a certain instant of time, its displacement is 0.01{tex} \mathrm { m } {/tex} and acceleration is {tex} 1.0 \mathrm { m } / \mathrm { s } ^ { 2 } . {/tex} The period of oscillation is

A

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

B

{tex} 0.2\mathrm { s } {/tex}

C

{tex} \frac { \pi } { 10 } \mathrm s {/tex}

{tex}\mathrm{\frac{\pi}{5}s}{/tex}

##### Explanation

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Q 12. The particle executing simple harmonic motion has a kinetic energy {tex} K _ { 0 } \cos ^ { 2 } \omega t . {/tex} The maximum values of the potential energy and the total energy are respectively

A

{tex} K _ { 0 } / 2 {/tex} and {tex} K _ { 0 } {/tex}

B

{tex} K _ { 0 } {/tex} and 2{tex} K _ { 0 } {/tex}

{tex} K _ { 0 } {/tex} and {tex} K _ { 0 } {/tex}

D

0 and 2{tex} K _ { 0 } {/tex}

##### Explanation

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Q 13. A simple pendulum attached to the ceiling of a stationary lift has a time period {tex}\mathrm { T } {/tex}. The distance {tex} y {/tex} covered by the lift moving upwards varies with time {tex} t {/tex} as {tex} y = t ^ { 2 } {/tex} where {tex} y {/tex} is in metres and {tex} t {/tex} in seconds. If {tex} \mathrm { g } = 10 \mathrm { m } / \mathrm { s } ^ { 2 } {/tex} , the time period of pendulum will be

A

{tex} \sqrt { \frac { 4 } { 5 } } \mathrm { T } {/tex}

{tex} \sqrt { \frac { 5 } { 6 } } \mathrm { T } {/tex}

C

{tex} \sqrt { \frac { 5 } { 4 } } \mathrm { T } {/tex}

D

{tex} \sqrt { \frac { 6 } { 5 } } \mathrm { T } {/tex}

##### Explanation

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Q 14. A particle moves with simple harmonic motion in a straight line. In first {tex} \tau {/tex} s, after starting from rest it travels a distance a, and in next {tex} \tau {/tex} s it travels 2a, in same direction, then:

A

amplitude of motion is 3{tex} \mathrm { a } {/tex}

B

time period of oscillations is 8{tex} \tau {/tex}

C

amplitude of motion is 4{tex} \mathrm { a } {/tex}

time period of oscillations is 6{tex} \tau {/tex}

##### Explanation

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Q 15. In damped oscillations, the amplitude of oscillations is reduced to one-third of its inital value {tex} a _ { 0 } {/tex} at the end of 100 oscillations. When the oscillator completes 200 oscillations, its amplitude must be

A

{tex} a _ { 0 } / 2 {/tex}

B

{tex} a _ { 0 } / 4 {/tex}

C

{tex} a _ { 0 } / 6 {/tex}

{tex} a _ { 0 } / 9 {/tex}

##### Explanation

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Q 16. The spring constant from the adjoining combination of springs is

A

{tex} \mathrm K {/tex}

B

{tex} \mathrm { 2K } {/tex}

{tex} \mathrm { 4K } {/tex}

D

{tex} \mathrm { 5K } / 2 {/tex}

##### Explanation

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Q 17. A simple harmonic wave having an amplitude a and time period {tex} \mathrm { T } {/tex} is represented by the equation {tex} y = 5 \sin \pi ( t + 4 ) m {/tex}
Then the value of amplitude {tex} (a) {/tex} in metre and time period {tex} ( \mathrm { T } ) {/tex} in second are

A

{tex} a = 10 , T = 2 {/tex}

B

{tex} a = 5 , T = 1 {/tex}

C

{tex} a = 10 , T = 1 {/tex}

{tex} a = 5 , T = 2 {/tex}

##### Explanation

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Q 18. A particle moves such that its acceleration {tex} { ' } \mathrm { a }{ ' } {/tex} is given by a {tex} = - \mathrm { zx } {/tex} where {tex} \mathrm { x } {/tex} is the displacement from equilibrium position and {tex} \mathrm { z } {/tex} is constant. The period of oscillation is

A

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

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

C

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

D

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

##### Explanation

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Q 19. The displacement of an object attached to a spring and executing simple harmonic motion is given by {tex} x = 2 \times 10 ^ { - 2 } {/tex}cos {tex} \pi t {/tex} metre. The time at which the maximum speed first occurs is

A

0.25 sec

0.5 sec

C

0.75 sec

D

0.125 sec

##### Explanation

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Q 20. A tunnel has been dug through the centre of the earth and a ball is released in it. It executes S.H.M. with time period

A

42 minutes

B

1 day

C

1 hour

84.6 minutes

##### Explanation

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Q 21. The displacement equation of a particle is {tex} x = 3 \sin 2 t + 4 \cos 2 t {/tex} . The amplitude and maximum velocity will be respectively

{tex} 5,10 {/tex}

B

{tex} 3,2 {/tex}

C

{tex} 4,2 {/tex}

D

{tex} 3,4 {/tex}

##### Explanation

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Q 22. A body of mass 0.01 kg executes simple harmonic motion about x = 0 under the influence of a force as shown in figure.The time period of SHM is

A

1.05{tex} \mathrm { s } {/tex}

B

0.52{tex} \mathrm { s } {/tex}

C

0.25

0.03{tex} \mathrm { s } {/tex}

##### Explanation

Slope of F-x curve = -k = - {tex} \large \frac {80}{0.2} {/tex} = 400N/m Time period, {tex}T{/tex} = {tex} 2\pi \sqrt {\frac {m}{k}} {/tex} = 0.03 s

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Q 23. Two oscillators are started simultaneously in same phase. After 50 oscillations of one, they get out of phase by {tex} \pi {/tex} , that
is half oscillation. The percentage difference of frequencies of the two oscillators is nearest to

A

2{tex} \% {/tex}

1{tex} \% {/tex}

C

0.5{tex} \% {/tex}

D

0.25{tex} \% {/tex}

##### Explanation

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Q 24. If the mass shown in figure is slightly displaced and then let go, then the system shall oscillate with a time period of

A

2{tex} \pi \sqrt { \frac { \mathrm { m } } { 3 \mathrm { k } } } {/tex}

2{tex} \pi \sqrt { \frac { 3 \mathrm m } { 2 \mathrm k } } {/tex}

C

2{tex} \pi \sqrt { \frac { 2 \mathrm { m } } { 3 \mathrm { k } } } {/tex}

D

2{tex} \pi \sqrt { \frac { 3 \mathrm { k } } { \mathrm { m } } } {/tex}

##### Explanation

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Q 25. Starting from the origin a body oscillates simple harmonically with a period of 2{tex} \mathrm { s } {/tex} . After what time will its kinetic energy be 75{tex} \% {/tex} of the total energy?

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

B

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

C

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

D

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