NEET > Oscillations and Waves

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


Q 1.    

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 2.    

Correct4

Incorrect-1

A mass is suspended separately by two different springs in successive order, then time periods is {tex} t _ { 1 } {/tex} and {tex} t _ { 2 } {/tex} respectively. It is connected by both springs as shown in fig. then time period is {tex} t _ { 0 } {/tex} . The correct relation is

A

{tex} t _ { 0 } ^ { 2 } = t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 } {/tex}

{tex} t _ { 0 } ^ { - 2 } = t _ { 1 } ^ { - 2 } + t _ { 2 } ^ { - 2 } {/tex}

C

{tex} \mathrm { t } _ { 0 } ^ { 1 } = \mathrm { t } _ { 1 } ^ { 1 } + \mathrm { t } _ { 2 } ^ { 1 } {/tex}

D

{tex} t _ { 0 } = t _ { 1 } + t _ { 2 } {/tex}

Explanation



Q 3.    

Correct4

Incorrect-1

A rod of length {tex} \ell {/tex} is in motion such that its ends {tex} A {/tex} and {tex} B {/tex} are moving along {tex} x {/tex} -axis and {tex} y {/tex} -axis respectively. It is given that {tex} \frac { \mathrm { d } \theta } { \mathrm { dt } } = 2 \mathrm { rad } / \mathrm { sec } {/tex} always. {tex} \mathrm { P } {/tex} is a fixed point on the rod. Let {tex} \mathrm { M } {/tex} be the projection of {tex} P {/tex} on {tex} x {/tex} -axis. For the time interval in which {tex} \theta {/tex} changes from 0 to {tex} \frac { \pi } { 2 } , {/tex} the correct statement is

A

The acceleration of {tex} \mathrm { M } {/tex} is always directed towards right

M executes SHM

C

M moves with constant speed

D

M moves with constant acceleration

Explanation



Q 4.    

Correct4

Incorrect-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



Q 5.    

Correct4

Incorrect-1

A mass M attached to a spring oscillates with a period of 2{tex} \mathrm { s } {/tex} . If the mass is increased by 2{tex} \mathrm { kg } {/tex} , then the period increases by 2{tex} \mathrm { s } {/tex} . Find the initial mass {tex} \mathrm { M } {/tex} assuming that Hooke's law is obeyed.

{tex} \frac { 2 } { 3 } \mathrm { kg } {/tex}

B

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

C

{tex} \frac { 1 } { 2 } \mathrm { kg } {/tex}

D

1{tex} \mathrm { kg } {/tex}

Explanation



Q 6.    

Correct4

Incorrect-1

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





Q 7.    

Correct4

Incorrect-1

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





Q 8.    

Correct4

Incorrect-1

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



Q 9.    

Correct4

Incorrect-1

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



Q 10.    

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

A

1{tex} \% {/tex}

B

21{tex} \% {/tex}

C

42{tex} \% {/tex}

10{tex} \% {/tex}

Explanation



Q 11.    

Correct4

Incorrect-1

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

Q 12.    

Correct4

Incorrect-1

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



Q 13.    

Correct4

Incorrect-1

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





Q 14.    

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}

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 15.    

Correct4

Incorrect-1

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

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

B

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

C

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

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

Explanation

Q 16.    

Correct4

Incorrect-1

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





Q 17.    

Correct4

Incorrect-1

A simple pendulum attached to the ceiling of a stationary lift has a time period T. The distance y 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 t 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



Q 18.    

Correct4

Incorrect-1

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} sit 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





Q 19.    

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 20.    

Correct4

Incorrect-1

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

A

{tex} \mathrm { L } _ { \mathrm { A } } = 2 \mathrm { L } _ { \mathrm { B } } \mathrm { and } \mathrm { M } _ { \mathrm { A } } = \mathrm { M } _ { \mathrm { B } } / 2 {/tex}

B

{tex} \mathrm { L } _ { \mathrm { A } } = 4 \mathrm { L } _ { \mathrm { B } } {/tex} regardless of masses

{tex} \mathrm { L } _ { \mathrm { A } } = \mathrm { L } _ { \mathrm { B } } / 4 {/tex} regardless of masses

D

{tex} \mathrm { L } _ { \mathrm { A } } = 2 \mathrm { L } _ { \mathrm { B } } {/tex} and {tex} \mathrm { M } _ { \mathrm { A } } = 2 \mathrm { M } _ { \mathrm { B } } {/tex}

Explanation

Q 21.    

Correct4

Incorrect-1

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

Q 22.    

Correct4

Incorrect-1

The spring constant from the adjoining combination of
Springs is

A

{tex} K {/tex}

B

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

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

D

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

Explanation

Q 23.    

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 x is maximum

D

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

Explanation

Q 24.    

Correct4

Incorrect-1

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 (a) in {tex} ( \mathrm { m } ) {/tex} 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



Q 25.    

Correct4

Incorrect-1

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