Paper 1 Oscillations and SHM Drills

Q1

The period of an oscillation is

A. maximum displacement from equilibrium.
B. number of oscillations per second.
C. time for one complete oscillation.
D. angular displacement per unit time.

Q2

If frequency is $2.5\mathrm{Hz}$, the period is

A. $0.20\mathrm{s}$
B. $0.40\mathrm{s}$
C. $2.5\mathrm{s}$
D. $5.0\mathrm{s}$

Q3

Angular frequency is related to frequency by

A. $\omega =f/2\pi$
B. $\omega =2\pi f$
C. $\omega =2\pi /f$
D. $\omega =f^2$

Q4

The defining condition for SHM is

A. velocity proportional to displacement and away from equilibrium.
B. acceleration proportional to displacement and directed towards equilibrium.
C. constant speed in a straight line.
D. constant acceleration.

Q5

For SHM, $a=-{\omega }^{2}x$. The gradient of a graph of $a$ against $x$ is

A. $\omega$
B. $-\omega$
C. ${\omega }^2$
D. $-{\omega }^2$

Q6

At maximum displacement in ideal SHM, speed is

A. maximum.
B. zero.
C. equal to acceleration.
D. independent of amplitude.

Q7

At equilibrium in ideal SHM, acceleration is

A. zero.
B. maximum.
C. equal to $\omega A$.
D. directed away from equilibrium.

Q8

For SHM with amplitude $A$, maximum speed is

A. $A/\omega$
B. $\omega A$
C. ${\omega }^{2}A$
D. $A^2\omega$

Q9

For a mass-spring oscillator, the period is

A. $2\pi \sqrt{m/k}$
B. $2\pi \sqrt{k/m}$
C. $m/k$
D. $k/m$

Q10

For a small-angle simple pendulum, the period depends mainly on

A. bob mass.
B. amplitude for all amplitudes.
C. length and gravitational field strength.
D. string tension only.

Q11

Damping causes oscillation amplitude to

A. increase indefinitely.
B. decrease with time.
C. stay exactly constant.
D. become negative.

Q12

Resonance occurs when steady-state amplitude is maximum as

A. driving frequency is varied.
B. mass is zero.
C. damping is infinite.
D. the system is not driven.

Q13

Increasing damping in a forced oscillator generally

A. makes the resonance peak lower and broader.
B. makes the peak infinitely high.
C. removes all restoring force.
D. increases amplitude at all frequencies.

Q14

In ideal SHM, total mechanical energy is proportional to

A. amplitude.
B. amplitude squared.
C. period.
D. displacement sign.

Q15

A time lag of $T/4$ corresponds to phase difference

A. $\pi /4$
B. $\pi /2$
C. $\pi$
D. $2\pi$

Q16

Two oscillations are in antiphase when their phase difference is

A. $0$
B. $\pi /2$
C. $\pi$
D. $2\pi$

Q17

In SHM, acceleration and displacement are

A. in the same direction.
B. always perpendicular.
C. in opposite directions.
D. unrelated.

Q18

At a turning point in ideal SHM, energy is mainly

A. kinetic.
B. potential.
C. thermal.
D. zero.

Q19

A displacement-time graph for undamped SHM is

A. sinusoidal.
B. linear.
C. exponential decay only.
D. a square wave.

Q20

The natural frequency of a system is the frequency at which it

A. is driven externally.
B. oscillates freely after being displaced and released.
C. dissipates no energy in all real cases.
D. has zero restoring force.