Question 1

Which of the following best describes the equation of motion for a simple harmonic oscillator with displacement $x(t)$?

Accepted Answer

$m \frac{d^2x}{dt^2} + kx = 0$

Question 2

A mass $m$ attached to a spring with spring constant $k$ oscillates with period $T$. Which formula gives the period of oscillation?

Accepted Answer

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

Question 3

For a simple pendulum of length $l$ under gravity $g$, what is the angular frequency $\omega$ for small oscillations?

Accepted Answer

$\omega = \sqrt{\frac{g}{l}}$

Question 4

A physical pendulum consists of a rigid body of mass $M$ and moment of inertia $I$ about the pivot. The distance from the pivot to the center of mass is $d$. What is the period $T$ for small oscillations?

Accepted Answer

$T = 2\pi \sqrt{\frac{I}{Mgd}}$

Question 5

A damped oscillator is described by $m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0$. What happens to the amplitude over time if the system is underdamped?

Accepted Answer

The amplitude decreases exponentially but oscillations persist.

Question 6

Which of the following is the general solution for the displacement $x(t)$ of a simple harmonic oscillator?

Accepted Answer

$x(t) = A \cos(\omega t + \phi)$

Question 7

A mass-spring system oscillates with amplitude $A$ and angular frequency $\omega$. What is the maximum speed of the mass?

Accepted Answer

$v_{max} = A \omega$

Question 8

For a simple pendulum, which assumption is necessary for the period formula $T = 2\pi \sqrt{\frac{l}{g}}$ to be valid?

Accepted Answer

The oscillations are small (small angle approximation).

Question 9

A uniform rod of length $L$ and mass $M$ is pivoted at one end. What is the period of small oscillations?

Accepted Answer

$T = 2\pi \sqrt{\frac{2L}{3g}}$

Question 10

Which of the following best describes the restoring force in a simple harmonic oscillator?

Accepted Answer

$F = -kx$

Question 11

A damped oscillator has a damping coefficient $b$ and mass $m$. What is the condition for critical damping?

Accepted Answer

$b^2 = 4mk$

Question 12

A mechanical wave travels along a string with speed $v$. If the tension in the string is $T$ and the mass per unit length is $\mu$, what is the wave speed?

Accepted Answer

$v = \sqrt{\frac{T}{\mu}}$

Question 13

Which of the following is true for the energy in a simple harmonic oscillator?

Accepted Answer

Total energy is constant and equals $\frac{1}{2}kA^2$

Question 14

A mass $m$ attached to a spring is displaced and released from rest at $x = A$. What is the velocity when it passes through equilibrium?

Accepted Answer

$v = \omega A$

Question 15

Which of the following best describes resonance in a driven oscillator?

Accepted Answer

The amplitude becomes maximum when the driving frequency matches the natural frequency.

Question 16

A wave on a string is described by $y(x,t) = A \sin(kx - \omega t)$. What is the phase velocity of the wave?

Accepted Answer

$v = \frac{\omega}{k}$

Question 17

If the amplitude of a damped oscillator drops from $A_0$ to $A_0/2$ in time $t$, what is the logarithmic decrement $\delta$?

Accepted Answer

$\delta = \ln 2$

Question 18

Which of the following is the correct expression for the kinetic energy of a simple harmonic oscillator at displacement $x$?

Accepted Answer

$K = \frac{1}{2}k(A^2 - x^2)$

Question 19

A sound wave travels in air at STP. What is the approximate speed of sound?

Accepted Answer

$343\ \mathrm{m/s}$

Question 20

Which of the following statements about mechanical waves is correct?

Accepted Answer

Mechanical waves require a medium to propagate.

Oscillations and Mechanical Waves: Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards