Online Test: Oscillations | Class 11 Physics

Question 1 of 18

Simple harmonic motion is characterised by the relation:

$a=\omega^2 x$

$a=-\omega^2 x$

$a=-\omega x$

$a=\omega x$

Explanation: In SHM acceleration is proportional to displacement and directed towards the mean position: $a=-\omega^2 x$.

Question 2 of 18

The displacement in SHM is $x=A\sin(\omega t+\phi)$. The quantity $\phi$ is called the:

amplitude

angular frequency

initial phase (epoch)

time period

Explanation: $\phi$ is the initial phase or epoch, the phase at $t=0$.

Question 3 of 18

The velocity of a particle in SHM is maximum at:

the extreme positions

the mean position

$x=A/2$

$x=A/\sqrt{2}$

Explanation: $v=\omega\sqrt{A^2-x^2}$ is greatest when $x=0$.

Question 4 of 18

The angular frequency $\omega$ is related to the period $T$ by:

$\omega=2\pi T$

$\omega=\frac{2\pi}{T}$

$\omega=\frac{T}{2\pi}$

$\omega=\pi T$

Explanation: $\omega=\frac{2\pi}{T}=2\pi f$.

Question 5 of 18

In SHM the acceleration is maximum at:

the mean position

the extreme positions

all positions

$x=A/2$

Explanation: $a=-\omega^2 x$ is largest in magnitude when $|x|=A$.

Question 6 of 18

The maximum velocity of a particle of amplitude $A$ and angular frequency $\omega$ in SHM is:

$A\omega^2$

$A\omega$

$\frac{A}{\omega}$

$\omega^2$

Explanation: $v_{max}=A\omega$ occurs at the mean position.

Question 7 of 18

The kinetic energy of an SHM particle at displacement $x$ is:

$\frac{1}{2}m\omega^2 x^2$

$\frac{1}{2}m\omega^2(A^2-x^2)$

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

$\frac{1}{2}m\omega^2(A^2+x^2)$

Explanation: $KE=\frac{1}{2}mv^2=\frac{1}{2}m\omega^2(A^2-x^2)$.

Question 8 of 18

The potential energy of a particle in SHM at displacement $x$ is:

$\frac{1}{2}m\omega^2 x^2$

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

$\frac{1}{2}m\omega^2(A^2-x^2)$

zero

Explanation: $PE=\frac{1}{2}m\omega^2 x^2=\frac{1}{2}kx^2$.

Question 9 of 18

The total mechanical energy of a particle in SHM is:

$\frac{1}{2}m\omega^2 x^2$

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

zero at the extremes

maximum at the mean position

Explanation: $E=KE+PE=\frac{1}{2}m\omega^2 A^2$ and is constant.

Question 10 of 18

KE equals PE in SHM at a displacement of:

$A$

$\frac{A}{2}$

$\frac{A}{\sqrt{2}}$

$0$

Explanation: Setting $KE=PE$ gives $A^2=2x^2$, so $x=\frac{A}{\sqrt{2}}$.

Question 11 of 18

The total energy of an SHM is proportional to:

$A$

$A^2$

$\frac{1}{A}$

$A^3$

Explanation: $E=\frac{1}{2}m\omega^2 A^2\propto A^2$.

Question 12 of 18

The time period of a spring–mass system is:

$2\pi\sqrt{\frac{k}{m}}$

$2\pi\sqrt{\frac{m}{k}}$

$2\pi\sqrt{\frac{L}{g}}$

$2\pi\sqrt{mk}$

Explanation: $T=2\pi\sqrt{\frac{m}{k}}$ from $\omega=\sqrt{k/m}$.

Question 13 of 18

The time period of a simple pendulum of length $L$ is:

$2\pi\sqrt{\frac{g}{L}}$

$2\pi\sqrt{\frac{L}{g}}$

$2\pi\sqrt{Lg}$

$2\pi\frac{L}{g}$

Explanation: $T=2\pi\sqrt{\frac{L}{g}}$ for small oscillations.

Question 14 of 18

A simple pendulum is taken to the Moon ($g$ smaller). Its time period will:

decrease

increase

stay the same

become zero

Explanation: Since $T\propto\frac{1}{\sqrt{g}}$, a smaller $g$ gives a larger period.

Question 15 of 18

Two identical springs of constant $k$ joined in series have an effective constant of:

$2k$

$k$

$\frac{k}{2}$

$4k$

Explanation: $\frac{1}{k_s}=\frac{1}{k}+\frac{1}{k}=\frac{2}{k}$, so $k_s=\frac{k}{2}$.

Question 16 of 18

In a damped oscillation, the amplitude:

remains constant

grows linearly

decreases exponentially with time

oscillates between two fixed values

Explanation: The amplitude decays as $A(t)=A_0 e^{-bt/2m}$.

Question 17 of 18

Resonance occurs when the frequency of the driving force is:

twice the natural frequency

half the natural frequency

equal to the natural frequency

zero

Explanation: Amplitude is maximum when the driving frequency equals the natural frequency.

Question 18 of 18

A body in SHM has period $T$. Its kinetic energy varies with a period of:

$T$

$\frac{T}{2}$

$2T$

$4T$

Explanation: KE (and PE) vary at twice the frequency of the motion, i.e. with period $\frac{T}{2}$.

Online Test — Oscillations