Oscillations PYQs

 

Section A – 1 Mark Questions

Q.1. A simple harmonic oscillator has amplitude 16 cm and period 4 seconds. The interval of time required by it to travel from x = 16 cm to x = 8 cm is _______. (July 2022)

(a) 1/2 second
(b) 2/3 second
(c) 5/6 second
(d) 4/3 second

Q.2. Periodic time of angular oscillations of a bar magnet is proportional to the _______. (July 2023)

(a) ratio of moment of inertia and magnetic field
(b) ratio of magnetic field and moment of inertia
(c) square root of the ratio of moment of inertia and magnetic field
(d) square root of the ratio of magnetic field and moment of inertia

Q.3. A body performing linear S.H.M. experiences a force of 0.2 N when displaced through 4 cm from the mean position. Its force constant will be _______. (July 2023)

(a) 2 N/m
(b) 2.5 N/m
(c) 5 N/m
(d) 8 N/m

Q.4. The velocity of bob of a second’s pendulum when it is 6 cm from its mean position and amplitude of 10 cm, is _______. (February 2024)

(A) 8π cm/s
(B) 6π cm/s
(C) 4π cm/s
(D) 2π cm/s

Q.5. The period of conical pendulum in terms of its length (l), semi-vertical angle (θ) and acceleration due to gravity (g) is _______. (February 2026)

Q.6. A particle is subjected to two parallel S.H.M.s such that x = 2 sin ωt and y = 2 sin (ωt + π/3). The amplitude of the resultant S.H.M. will be _______. (February 2026)

(a) 0
(b) 2√3
(c) 4
(d) 12

Very Short Answer Questions

Q.7. Write the differential equation for angular S.H.M. (March 2022)

Q.8. Calculate the velocity of a particle performing S.H.M. after 1 second, if its displacement is given by \(x=5\sin\left(\frac{\pi t}{3}\right)\) m. (February 2023)

Q.9. Calculate the period of a particle performing linear S.H.M. with maximum speed of 0.08 m/s and maximum acceleration of 0.32 m/s². (July 2023)

Q.10. Write the differential equation for linear S.H.M. (July 2024)

Q.11. A body of mass 0.2 kg performs linear S.H.M. It experiences a restoring force of 0.4 N when its displacement from the mean position is 8 cm. Determine force constant. (July 2024)

Q.12. What is the velocity of a particle performing linear SHM, at extreme position? (June 2025)

Q.13. Calculate the maximum velocity of a particle having amplitude of oscillation 4 cm and period 4 seconds. (July 2026)

Section B – 2 Marks Questions

Q.14. Distinguish between free vibrations and forced vibrations (Two points). (February 2023)

Q.15. Obtain the differential equation of linear simple harmonic motion. (February 2024)

Q.16. A bar magnet of moment of inertia of 500 gcm² oscillates with a time period of 3.142 seconds in a horizontal plane. What is its magnetic moment if the horizontal component of earth’s magnetic field is 4 × 10⁻⁵ T? (July 2024)

Q.17. A body of mass 0.8 kg performs linear S.H.M. It experiences a restoring force of 0.4 N, when its displacement from mean position is 4 cm. Determine Force constant and Period of S.H.M. (February 2025)

Q.18. Draw a neat labelled diagram of variation of kinetic energy and potential energy with displacement in S.H.M. (June 2025)

Q.19. The differential equation of linear S.H.M. in SI units is \(\frac{d^2x}{dt^2}=-36x\). Calculate its frequency and periodic time. (June 2025)

Q.20. Distinguish between free and forced vibrations. (July 2026)

Section C – 3 Marks Questions

Q.21. State the differential equation of linear S.H.M. Hence, obtain expression for:

(i) acceleration
(ii) velocity

(February 2023)

Q.22. Obtain the expression for the period of simple pendulum performing S.H.M. (July 2023)

Q.23. At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 10 cm, three times its potential energy? (July 2024)

Q.24. Obtain an expression for the period of a bar magnet vibrating in a uniform magnetic field, performing S.H.M. (February 2025)

Q.25. Obtain an expression for period of a bar magnet vibrating in a uniform magnetic field and performing angular S.H.M. (February 2026)

Section D – 4 Marks Questions

Q.26. Define second’s pendulum. Derive a formula for the length of second’s pendulum.

A particle performing linear S.H.M. has maximum velocity 25 cm/s and maximum acceleration 100 cm/s². Find period of oscillations. (March 2022)

Q.27. Distinguish between an ammeter and a voltmeter. (Two points each).

The displacement of a particle performing simple harmonic motion is 1/3rd of its amplitude. What fraction of total energy will be its kinetic energy? (February 2024)

The February 2024 question is reproduced with its original mixed-chapter parts.

Q.28. State differential equation of linear S.H.M. hence obtain an expression for acceleration, velocity and displacement of a particle performing S.H.M. (July 2026)