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Oscillations — NEET & JEE MCQs with answers
Oscillations are periodic to-and-fro motions about an equilibrium position. This chapter covers simple harmonic motion (SHM) as the fundamental model of oscillation, its kinematic equations, energy, and the simple pendulum, as well as the connection between SHM and uniform circular motion.
Topics in this chapter
- 13.1 Introduction
- 13.2 Periodic and Oscillatory Motion
- 13.3 Simple Harmonic Motion
- 13.4 Simple Harmonic Motion and Uniform Circular Motion
- 13.5 Velocity and Acceleration in Simple Harmonic Motion
- 13.6 Force Law for Simple Harmonic Motion
- 13.7 Energy in Simple Harmonic Motion
- 13.8 The Simple Pendulum
Free practice questions
A block of mass $m=5\ \text{kg}$ oscillates under the force law $F=-kx$ with $k=180\ \text{N m}^{-1}$. Its time period is
- A. $12\pi\ \text{s}$
- B. $\frac{\pi}{6}\ \text{s}$
- C. $\frac{\pi}{3}\ \text{s}$
- D. $\frac{2\pi}{3}\ \text{s}$
Show answer
Answer: C — $\omega=\sqrt{k/m}=6\ \text{rad s}^{-1}$, so $T=2\pi\sqrt{m/k}=\dfrac{2\pi}{6}=\frac{\pi}{3}\ \text{s}\approx1.05\ \text{s}$.
NCERT Class 11 Physics Ch 13
Which one of the following is periodic but not oscillatory?
- A. A ball oscillating in a bowl
- B. A mass on a vibrating spring
- C. A swinging pendulum
- D. The motion of the second hand of a clock around its dial
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Answer: D — NCERT: circular motion (e.g. uniform circular motion / hands of a clock revolving) is periodic but not oscillatory; pendulum and spring-mass are oscillatory.
NCERT Class 11 Physics · Ch 13 · 13.2 Periodic and Oscillatory Motion
In SHM the velocity leads (is ahead of) the displacement in phase by:
- A. $\pi/2$
- B. $\pi$
- C. $\pi/4$
- D. $0$
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Answer: A — $x=A\cos\omega t$ and $v=-\omega A\sin\omega t=\omega A\cos(\omega t+\pi/2)$, so velocity is ahead of displacement by $\pi/2$.
NCERT Class 11 Physics · Ch 13 · 13.4 Simple Harmonic Motion and Uniform Circular Motion
Taking $g=\pi^2\ \text{m s}^{-2}$, a simple pendulum of length $20.25\ \text{m}$ has a time period of:
- A. $10\ \text{s}$
- B. $18\ \text{s}$
- C. $8\ \text{s}$
- D. $9\ \text{s}$
Show answer
Answer: D — $T=2\pi\sqrt{20.25/\pi^2}=2\sqrt{20.25}=9$ s.
NCERT Class 11 Physics · Ch 13 · 13.8 The Simple Pendulum
A particle executes SHM of amplitude $A=0.2\ \text{m}$ with angular frequency $\omega=5\ \text{rad s}^{-1}$. Its maximum speed is
- A. $1\ \text{m s}^{-1}$
- B. $5\ \text{m s}^{-1}$
- C. $0.5\ \text{m s}^{-1}$
- D. $0.04\ \text{m s}^{-1}$
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Answer: A — The maximum speed in SHM is $|v|_{\max}=\omega A=5\times0.2=1\ \text{m s}^{-1}$, attained at the mean position.
NCERT Class 11 Physics Ch 13
A particle in SHM has spring constant $k = 100\ \text{N m}^{-1}$ and amplitude $A = 0.1\ \text{m}$. When it is at displacement $x = 0.06\ \text{m}$ from the mean position, its kinetic energy is
- A. $0.32\ \text{J}$
- B. $0.64\ \text{J}$
- C. $0.5\ \text{J}$
- D. $0.18\ \text{J}$
Show answer
Answer: A — Total $E = \tfrac12 kA^2 = 0.5$ J, PE $= \tfrac12 kx^2 = 0.18$ J. KE $= E - U = \tfrac12 k(A^2 - x^2) = 0.32$ J.
NCERT Class 11 Physics · Ch 13 · 13.7 Energy in Simple Harmonic Motion
The chapter introduction describes rectilinear motion and the motion of a projectile as examples of motion that is:
- A. repetitive with a fixed period
- B. periodic but not oscillatory
- C. oscillatory about a mean position
- D. non-repetitive
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Answer: D — The introduction states that we have already learnt about rectilinear motion and the motion of a projectile, and that **both these motions are non-repetitive**.
NCERT Class 11 Physics Ch 13
A particle executes SHM described by $x(t) = 5\cos(\omega t + \phi)\ \mathrm{cm}$. At an instant when the phase $(\omega t + \phi) = 3\pi/2\ \mathrm{rad}$, the displacement of the particle is:
- A. $5\ \mathrm{cm}$
- B. $0\ \mathrm{cm}$
- C. $-5\ \mathrm{cm}$
- D. $2.5\ \mathrm{cm}$
Show answer
Answer: B — Substituting the phase into $x = A\cos(\omega t+\phi)$: $x = 5\cos(3\pi/2) = 5 \times 0 = 0\ \mathrm{cm}$.
NCERT Class 11 Physics Ch 13
A spring-mass system has $m=0.25\,\text{kg}$ and $k=100\,\text{N m}^{-1}$. The frequency of oscillation is approximately:
- A. $3.18\,\text{Hz}$
- B. $1.59\,\text{Hz}$
- C. $6.37\,\text{Hz}$
- D. $20\,\text{Hz}$
Show answer
Answer: A — $\omega=\sqrt{k/m}=\sqrt{100/0.25}=\sqrt{400}=20\,\text{rad s}^{-1}$; $\nu=\omega/2\pi=20/(2\pi)=10/\pi\approx3.18\,\text{Hz}$.
NCERT Class 11 Physics · Ch 13 · 13.4 Simple Harmonic Motion and Uniform Circular Motion
Two simple pendulums of lengths $1\ \text{m}$ and $9\ \text{m}$ are at the same place. The ratio of their frequencies $f_1:f_2$ is:
- A. 1:9
- B. 3:1
- C. 1:3
- D. 9:1
Show answer
Answer: B — $f\propto1/\sqrt{L}$, so $f_1:f_2=\sqrt{L_2}:\sqrt{L_1}=\sqrt{9}:\sqrt{1}=3:1$.
NCERT Class 11 Physics · Ch 13 · 13.8 The Simple Pendulum
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