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JEE • PHYSICS • OSCILLATIONS

Oscillations practice · Hard

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Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

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1 Hard

1 of 8

Understanding +4 | -1

The displacement, velocity and acceleration in a simple harmonic motion are related as the

View answer and explanation

Correct option: A

displacement, velocity and acceleration all act in the same direction

Option A (displacement, velocity and acceleration all act in the same direction) is the correct answer because in SHM, at extreme positions, all three quantities point towards the mean position.

2 Hard

2 of 8

Understanding +4 | -1

Given below are two statements:
Statement I A second’s pendulum has a time period of

1\,s

.
Statement II It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the option given below.

View answer and explanation

Correct option: B

Statement I is false but statement II is true.

Statement B is correct because Statement I is false (second's pendulum has a period of 2s) and Statement II is true (time between extremes is half the period, or 1s).

3 Hard

3 of 8

Application +4 | -1

When an oscillator completes 100 oscillations its amplitude reduced to

\frac{1}{3}

of the initial value. What will be its amplitude when it completes 200 oscillations?

View answer and explanation

Correct option: D

\frac{1}{9}

Option D (

\frac{{1}}{{9}}

) is correct because the amplitude decays exponentially, and after 200 oscillations, it's reduced to one-ninth of the initial value.

4 Hard

4 of 8

Application +4 | -1

In damped oscillations, the amplitude of oscillations is reduced to one-third of its initial value

\mathrm{a}_0

at the end of 100 oscillations. Initial energy is

\mathrm{E}_0

. When the oscillator completes 200 oscillations, its energy must be

View answer and explanation

Correct option: D

\mathrm{E}_0 / 81

Option D (E₀ / 81) is correct because the energy is proportional to the square of the amplitude, and the amplitude is reduced to one-ninth after 200 oscillations.

5 Hard

5 of 8

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 is the phase difference calculated at t=0.5s using the given SHM equations.

6 Hard

6 of 8

Application +4 | -1

A particle performs simple harmonic motion with amplitude

A

. Its speed is tripled at the instant that it is at a distance

\frac{2}{3}A

from equilibrium position. The new amplitude of the motion is

View answer and explanation

Correct option: D

\frac{7}{3}A

Option D (

\frac{7}{3}A

) is correct because it's derived from applying the conservation of energy principle in SHM, considering the change in velocity and amplitude.

7 Hard

7 of 8

Analyzing +4 | -1

The equation of a travelling wave is

y=15 \sin ^2(3 x-4 t),

where

x, y

are in meter and

t

is in second. The amplitude of oscillation of particle is:

View answer and explanation

Correct option: B

7.5 m

Option B (7.5 m) is correct. By using the trigonometric identity to rewrite the equation, the amplitude of the oscillation is found to be 7.5 m.

8 Hard

8 of 8

Analyzing +4 | -1

I. Average kinetic energy in one oscillation during SHM of a body is

\frac{1}{4} m \omega^2 A^2

.

II. Maximum kinetic energy is

\frac{1}{2} m \omega^2 A^2

.

Which of the following statement(s) is/are correct?

View answer and explanation

Correct option: C

Both I and II

Option C (Both I and II) is correct because both the average kinetic energy and the maximum kinetic energy formulas are correctly stated for SHM.

Revision notes and key takeaways

Review OSCILLATIONS in your textbook or class notes, then use this set to check your understanding.

Key Takeaways

✓ This set contains 8 single-correct-answer MCQs on OSCILLATIONS.
✓ Try each question before opening its answer. Read the explanation where one is available.
✓ Sign in to save submitted answers. Revisit incorrect answers alongside your textbook or class notes.

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