Question 1

Which of the following best describes simple harmonic motion (SHM)?

Accepted Answer

A motion where the restoring force is proportional to the displacement and directed toward equilibrium.

Question 2

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates with amplitude $$A. $$What is the period $$T of $$the oscillation?

Accepted Answer

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

Question 3

Which equation gives the position $$x(t) of a $$particle in SHM with amplitude $$A$$, angular frequency $$\omega$$, and phase constant $$\phi$$?

Accepted Answer

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

Question 4

The maximum speed $$v_{max} of a $$mass in SHM is given by:

Accepted Answer

$$v_{max} = \omega A$$

Question 5

A pendulum of length $$L$$ swings with small amplitude. What is the period $$T of $$its oscillation?

Accepted Answer

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

Question 6

Which of the following statements about energy in SHM is correct?

Accepted Answer

The total mechanical energy is constant and equals $$\frac{1}{2}kA^2$.

Question 7

A block of mass $$m$$ oscillates vertically on a spring. If the spring constant is doubled, what happens to the period?

Accepted Answer

It decreases by a factor of $$\sqrt{2}.$$

Question 8

For a damped oscillator, which equation describes the amplitude as a function of time?

Accepted Answer

$$A(t) = A_0$ e$$^{-bt/2m}$$

Question 9

A physical pendulum has moment of inertia $$I$$ and mass $$m$$ with the center of mass a distance $$d$$ from the pivot. What is the period $$T$$?

Accepted Answer

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

Question 10

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

Accepted Answer

The amplitude of oscillation is maximized when the driving frequency matches the natural frequency.

Question 11

The equation for the acceleration $$a(t) of a $$mass in SHM is:

Accepted Answer

$$a(t) = -\$$omega^2$$ x(t)$$

Question 12

If a mass-spring system has a total energy $$E$$ and amplitude $$A$$, what is the spring constant $$k$$?

Accepted Answer

$$k = \frac{2E}{A^2$}$$

Question 13

Which of the following is true for the velocity and acceleration graphs of a mass in SHM?

Accepted Answer

Velocity leads position by $$\frac{\pi}{2}$$ and acceleration leads velocity by $$\frac{\pi}{2}.$$

Question 14

A lightly damped oscillator loses mechanical energy according to which law?

Accepted Answer

$$E(t) = E_0$ e$$^{-bt/m}$$

Question 15

Which of the following is a correct statement about the small-angle approximation for a pendulum?

Accepted Answer

It is valid only for angles less than about $$10^\circ.$$

Question 16

In coupled oscillators, what is a normal mode?

Accepted Answer

A mode in which all parts of the system oscillate with the same frequency and a fixed pattern.

Question 17

A mass $$m$$ attached to a spring is released from rest at $$x = A. $$What is the phase constant $$\phi in $$the equation $$x(t) = A \cos(\omega t + \phi)$$?

Accepted Answer

$$\phi = 0$$

Question 18

Which of the following best describes the effect of increasing the damping coefficient $$b in a $$damped oscillator?

Accepted Answer

The amplitude decays more rapidly.

Question 19

A mass-spring system oscillates with amplitude $$A$$ and angular frequency $$\omega. At $$what displacement is the kinetic energy equal to the potential energy?

Accepted Answer

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

Question 20

Which of the following is true for the resonance curve of a lightly damped oscillator?

Accepted Answer

The resonance peak is sharp and the maximum amplitude is high.

Oscillations: Simple Harmonic Motion, Damped and Driven Oscillations

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