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Oscillations practice · Mixed difficulty

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Showing 1-30 of 164 questions

1 Medium

1 of 164

Application +4 | -1

A mass m is suspended from a spring of length l and force constant K. The frequency of vibration of the mass is

{f_1}

. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is

{f_2}

. Which of the following relations between the frequencies is correct

View answer and explanation

Correct option: D

{f_2} = \sqrt 2 {f_1}

Option D (

{f_2} = \sqrt 2 {f_1}

) is correct because cutting the spring in half doubles the spring constant, which increases the frequency by a factor of

\sqrt{2}

2 Medium

2 of 164

Understanding +4 | -1

The time period of a loaded spring on earth is 6s. On the surface of moon, the time period of the same loaded spring will be.

View answer and explanation

Correct option: D

6 s

Option D (6 s) is correct because the time period of a spring-mass system depends on the mass and spring constant, which remain the same on the Moon.

3 Easy

3 of 164

Analyzing +4 | -1

Under the action of a force

F=-k x^3

, the motion of a particle is

(k=

a positive constant

)

View answer and explanation

Correct option: D

periodic but not simple harmonic

Option D (periodic but not simple harmonic) is correct because the force is proportional to

x^3

, not

x

, which is required for SHM, but the motion will still repeat.

4 Medium

4 of 164

Analyzing +4 | -1

S-I: A particle executes SHM with frequency

f

. The frequency with which total mechanical energy of particle oscillates is

2 f

.
S-II: Both kinetic as well as potential energy of particle in SHM oscillate with a frequency

2 f.

View answer and explanation

Correct option: D

S-I is false

\&

S-II is true

Option D (S-I is false & S-II is true) is correct because the frequency of oscillation of total mechanical energy is constant, while kinetic and potential energies oscillate at twice the frequency of SHM.

5 Hard

5 of 164

Application +4 | -1

The phase difference (in radian) between two SHM whose equations are

y_1=10 \sin \left(10 \pi t+\frac{\pi}{3}\right)

and

y_2=12 \sin \left(8 \pi t+\frac{\pi}{4}\right)

t=0.5 \mathrm{~s}

is:

View answer and explanation

Correct option: B

\frac{13 \pi}{12}

Option B (

\frac{{13 \pi}}{{12}}

) is correct because it represents the phase difference calculated at t=0.5s between the two given SHM equations.

6 Easy

6 of 164

Analyzing +4 | -1

A vertical spring block system is made to oscillate.
Statement-1: Its time period on earth is more than that on the moon.
Statement-2: Its extension on earth (in equilibrium) is more than that on the moon.

View answer and explanation

Correct option: D

Statement-1 is false, Statement-2 is true

Statement-1 is false, Statement-2 is true. The time period of a spring-block system is independent of gravity, while the extension in equilibrium depends on gravity.

7 Medium

7 of 164

Application +4 | -1

A particle of mass m is executing oscillations about the origin on the x-axis. Its potential energy is

U\left( x \right) = k{\left[ x \right]^3}

, where k is a positive constant. If the amplitude of oscillation is a, then its time period T is

View answer and explanation

Correct option: A

Proportional to

\frac{1}{{\sqrt a }}

Option A (Proportional to

\frac{1}{{\sqrt a }}

) is correct because the time period of oscillation is inversely proportional to the square root of the amplitude when the potential energy is proportional to

x^3

8 Medium

8 of 164

Analyzing +4 | -1

A particle moves according to the law,

x = rcos\frac{{\pi t}}{{2.}}

The distance covered by it the time interval between t= 0 to t=3s is

View answer and explanation

Correct option: C

3r

Option C (3r) is correct because the particle travels a distance of 'r' from t=0 to t=1, then returns 'r' from t=1 to t=2, and then travels another 'r' from t=2 to t=3, resulting in a total distance of 3r.

9 Medium

9 of 164

Understanding +4 | -1

(A): Since and cosine functions are periodic functions
(R): Sinusoidal functions repeat its values after a definite interval of time

View answer and explanation

Correct option: A

If Both A

\&

R are true and R is correct explanation of A

Option A (If Both A & R are true and R is correct explanation of A) is correct because both the assertion and the reason are true, and the reason correctly explains why sine and cosine functions are periodic.

10 Medium

10 of 164

Application +4 | -1

Velocity of a simple harmonic oscillation is given by

V = \sqrt {144 - 16{x^2}} {\mkern 1mu} {\mkern 1mu} m{s^{ - 1}}

where x is displacement in metre. Then maximum velocity of that oscillator is

View answer and explanation

Correct option: B

12\,\,m{s^{ - 1}}

Option B (

12\,m{s^{ - 1}}

) is correct because the maximum velocity of the oscillator is found by comparing the given equation with the standard form of velocity in SHM.

11 Medium

11 of 164

Remembering +4 | -1

Which one of the following is the correct relation between frequency

\mathrm{f}

and angular frequency

\omega

View answer and explanation

Correct option: B

\omega=2 \pi \mathrm{f}

Option B (

\omega=2 \pi \mathrm{f}

) is correct because it is the fundamental relationship between angular frequency and frequency.

12 Medium

12 of 164

Analyzing +4 | -1

The bob of a pendulum is in the lowest position and has a horizontal velocity of

\sqrt {gL}

where

L

is length of the pendulum and

g

is acceleration due to gravity is given to it. Then the bob

View answer and explanation

Correct option: C

Oscillates about the lowest position as mean position

Option C (Oscillates about the lowest position as mean position) is correct because the initial velocity is not high enough for the bob to complete a full circle.

13 Medium

13 of 164

Remembering +4 | -1

The differential equation of a particle executing simple harmonic motion along

y

-axis is

View answer and explanation

Correct option: A

\frac{d^2 y}{d t^2}+\omega^2 y=0

Option A (

\frac{{d^2 y}}{{d t^2}}+\omega^2 y=0

) is correct because it represents the standard differential equation for SHM.

14 Medium

14 of 164

Analyzing +4 | -1

The displacement

y

of a particle is given by

y=4 \cos ^2\left(\frac{t}{2}\right) \sin (1000 t)

. This expression may be considered to be a result of the superposition of how many simple harmonic motion

View answer and explanation

Correct option: A

Option A (3) is correct because the given expression can be simplified using trigonometric identities to a superposition of three simple harmonic motions.

15 Medium

15 of 164

Application +4 | -1

An object on a spring vibrates in a simple harmonic motion at a frequency of 4 hertz and an amplitude of 8 cm. If the mass of the object is 200 g, the spring constant is

View answer and explanation

Correct option: C

126 N/m

Option C (126 N/m) is correct because it is calculated using the frequency and mass to find the spring constant.

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16 Medium

16 of 164

Understanding +4 | -1

The average acceleration of a particle performing SHM over one complete oscillation is

View answer and explanation

Correct option: C

Zero

Option C (Zero) is correct because the velocity changes direction over the oscillation, resulting in zero average acceleration.

17 Medium

17 of 164

Application +4 | -1

The time period of a particle performing linear SHM is 18s. What is the time taken by it to make a displacement equal to half its amplitude from its equilibrium position ?

View answer and explanation

Correct option: C

\frac{3}{2}s

Option C (

\frac{3}{2}s

) is correct because it is calculated using the SHM equation and the given time period.

18 Medium

18 of 164

Remembering +4 | -1

Maximum acceleration in SHM

View answer and explanation

Correct option: A

\omega^2 A

Option A (

\omega^2 A

) is correct because the maximum acceleration in SHM is given by the formula

a_{max} = \omega^2 A

19 Medium

19 of 164

Application +4 | -1

The bob of a simple pendulum of mass m is displaced from its equilibrium position through height ‘h’ and then released. It vibrates with a time period of 2 seconds. The tension in the bob when the bob passes through mean position

View answer and explanation

Correct option: A

m\left( {g + 2{\pi ^2}h} \right)

Option A (

m(g + 2{\pi ^2}h)

) is correct because the tension at the mean position is the sum of the weight and the centripetal force, which depends on the height 'h' and the time period.

20 Easy

20 of 164

Application +4 | -1

If potential energy function for the force between two atoms in a diatomic molecule is approximately given by

U(x)=\frac{a}{x^8}-\frac{\mathrm{b}}{x^4}

, where a and

\mathrm{b}

are constants in standard SI units and

x

is in metres. Find the dissociation energy of the molecule (in

\mathrm{J}

). [Take a

=4 \mathrm{~J}

{ }^8

and

\mathrm{b}=20 \mathrm{~J} \mathrm{~m}^4

]

View answer and explanation

Correct option: A

Option A (25) is correct because the dissociation energy is calculated by finding the minimum potential energy of the molecule.

21 Medium

21 of 164

Analyzing +4 | -1

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

View answer and explanation

Correct option: B

\frac{{aT}}{x}

Option D (Non simple harmonic motion) is correct because the given displacement equation does not represent SHM.

22 Easy

22 of 164

Analyzing +4 | -1

A small ball is dropped from a certain height on the surface of a non-viscous liquid of density less than the density of ball. The motion of the ball is

View answer and explanation

Correct option: B

periodic but not SHM

Option B (periodic but not SHM) is correct because the ball will oscillate, but the restoring force is not proportional to the displacement.

23 Medium

23 of 164

Understanding +4 | -1

If a body is executing simple harmonic motion then

View answer and explanation

Correct option: C

At equilibrium position, the total energy is in the form of kinetic energy

Option C (At equilibrium position, the total energy is in the form of kinetic energy) is correct because at the equilibrium position, the potential energy is zero, and all the energy is kinetic.

24 Medium

24 of 164

Understanding +4 | -1

Consider the following statements : The total energy of a particle executing simple harmonic motion depends on its I. Amplitude II. Period III. Displacement Of these statements

View answer and explanation

Correct option: A

I and II are correct

Option A (I and II are correct) is correct because the total energy in SHM depends on amplitude and period, but not instantaneous displacement.

25 Medium

25 of 164

Analyzing +4 | -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

View answer and explanation

Correct option: C

First increase and then decrease to the original value

Option C (First increase and then decrease to the original value) is correct because as water flows out, the center of mass initially lowers, increasing the effective length, and then rises, decreasing the effective length, returning to the original value.

26 Medium

26 of 164

Application +4 | -1

A point performs simple harmonic oscillation of period T and the equation of motion is given by

x = a\,\,\,\sin \,\,\left( {w + \pi /6} \right)

After the elapse of what fraction of the time period the velocity of the point will be equal to half its maximum velocity

View answer and explanation

Correct option: B

\frac{T}{{12}}

Option B (

\frac{T}{{12}}

) is correct because it involves finding the time when velocity is half of maximum velocity in SHM.

27 Medium

27 of 164

Application +4 | -1

Two simple pendulums first of bob mass

{M_1}

and length

{L_1}

second of bob mass

{M_2}

and length

{L_2}

{M_1}

{M_2}

and

{L_1}

{2L_2}

. If the vibrational energy of both is same. Then which is correct

View answer and explanation

Correct option: B

Amplitude of B smaller than A

Option B, Amplitude of B smaller than A, is correct because for the same vibrational energy, the pendulum with a shorter length (and thus higher frequency) will have a smaller amplitude.

28 Easy

28 of 164

Application +4 | -1

A particle starts oscillation from origin on

x

-axis with period of oscillation (6) sec and amplitude

A

. If time taken by particle to reach from

x=A

x=\frac{\sqrt{3}}{2} A

for the first time is

\tau

then. Value of

6 \tau

is sec.

View answer and explanation

Correct option: C

Option C (3) is correct because the time taken to go from A to

\frac{\sqrt{3}}{2}A

is T/12, and T = 6s, so

\tau

= 6/12 = 0.5s. Therefore, 6

\tau

= 3.

29 Medium

29 of 164

Analyzing +4 | -1

A particle executes SHM, the graph of velocity as a function of displacement is

View answer and explanation

Correct option: C

an ellipse

Option C (an ellipse) is correct because the relationship between velocity and displacement in SHM is described by an ellipse equation.

30 Medium

30 of 164

Analyzing +4 | -1

The displacement of a particle along the

{x}

-axis is given by The motion of the particle corresponds to

View answer and explanation

Correct option: C

Non simple harmonic motion

Option C (Non simple harmonic motion) is correct because the given displacement equation is not in the form of a simple harmonic function (sine or cosine).

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