Question 1

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

Accepted Answer

Motion that repeats itself at regular intervals and is described by a sinusoidal function.

Question 2

A mass $$m$$ attached to a spring with spring constant $$k$$ oscillates horizontally on a frictionless surface. What is the angular frequency $$\omega of $$the oscillation?

Accepted Answer

$$\omega = \sqrt{\frac{k}{m}}$$

Question 3

Which of the following statements about the energy in a simple harmonic oscillator is correct?

Accepted Answer

The total mechanical energy is constant and proportional to the square of the amplitude.

Question 4

A pendulum of length $$l$$ and mass $$m$$ swings with small amplitude. What is the period $$T of $$its oscillation?

Accepted Answer

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

Question 5

If the amplitude of a mass-spring oscillator is doubled, how does the total mechanical energy change?

Accepted Answer

It increases by a factor of 4.

Question 6

Which force acts as the restoring force for a simple pendulum displaced from equilibrium?

Accepted Answer

The component of gravity perpendicular to the string: $$F = -mg\sin	heta$$

Question 7

A block of mass $$0.50\ \mathrm{kg} is $$attached to a spring with $$k = 14\ \mathrm{N/m}$$ and pulled $$30\ \mathrm{mm}$$ from equilibrium, then released from rest. What is the amplitude $$A of $$the resulting oscillation?

Accepted Answer

$$A = 0.030\ \mathrm{m}$$

Question 8

Which of the following is true about the period $$T of a $$simple harmonic oscillator?

Accepted Answer

It is independent of the amplitude.

Question 9

At the maximum displacement of a mass-spring system, what are the velocity and acceleration of the mass?

Accepted Answer

Velocity is zero, acceleration is maximum.

Question 10

A mass on a spring oscillates with position $$x(t) = A\sin(\omega t + \phi_i). $$What is the expression for its velocity as a function of time?

Accepted Answer

$$v_x(t) = \omega A \cos(\omega t + \phi_i)$$

Question 11

Which of the following best explains why an ideal spring oscillator does not stop when it first reaches equilibrium?

Accepted Answer

It has kinetic energy at equilibrium, so it continues moving.

Question 12

For a simple harmonic oscillator, what is the relationship between acceleration $$a_x$$ and displacement $$x$$?

Accepted Answer

$$a_x = -\$$omega^2$$ x$$

Question 13

A guitar string is plucked harder, increasing its amplitude. What happens to the frequency of the sound produced?

Accepted Answer

The frequency remains the same.

Question 14

A block of mass $$m is $$suspended from a vertical spring of spring constant $$k. $$How far below the relaxed position is the equilibrium position?

Accepted Answer

$$x_{eq} = \frac{mg}{k}$$

Question 15

Which of the following is a correct statement about the period of a simple pendulum?

Accepted Answer

It is independent of the mass of the pendulum.

Question 16

A mass-spring system oscillates with $$x(t) = A\sin(\omega t). At $$what position is the kinetic energy maximized?

Accepted Answer

At $$x = 0$$

Question 17

A mass $$m on a $$spring with spring constant $$k is $$oscillating. If the mass is increased, what happens to the period $$T$$?

Accepted Answer

The period increases.

Question 18

Which of the following is a real-world example of a system that can be modeled as a simple harmonic oscillator?

Accepted Answer

A ball rolling back and forth in a bowl.

Question 19

The equation for the total energy $$E of a $$simple harmonic oscillator is:

Accepted Answer

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

Chapter 15: Periodic Motion – Principles and Practice of Physics

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