Q: A building sways in the wind with amplitude $$A = 0.40\ \text{m}$$ and period $$T = 7.7\ \text{s}. $$What is the maximum acceleration of the top of the building?

$$a_{\text{max}} = (2\pi f)^2$ A$$

Question 1

A monkey swings from a branch, moving back and forth in a regular pattern. Which type of motion best describes the swinging of the monkey, and what determines the period of this motion?

Accepted Answer

Simple harmonic motion; the period depends on the length of the 'pendulum' (the monkey's arms and body) and the acceleration due to gravity.

Question 2

A marble is placed at the bottom of a spherical bowl and then displaced to one side. According to the diagrams, what is the direction of the net force acting on the marble when it is away from equilibrium?

Accepted Answer

Toward the equilibrium position, acting as a restoring force.

Question 3

Which of the following best describes the relationship between period $$T$$ and frequency $$f$$ for any oscillatory motion?

Accepted Answer

$$T = \frac{1}{f}$$

Question 4

A mass $$m is $$attached to a spring with spring constant $$k$$ and oscillates horizontally. Which equation gives the restoring force acting on the mass when it is displaced by $$x$$ from equilibrium?

Accepted Answer

$$(F_{	ext{net}})_x = -kx$$

Question 5

A 25 g mass is hung from a spring, stretching it by 5.0 cm. What is the spring constant $$k of $$the spring? (Use $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$k = 4.9\ 	ext{N/m}$$

Question 6

A mass oscillates on a spring with amplitude $$A$$ and frequency $$f. $$What is the equation for its maximum speed?

Accepted Answer

$$v_{	ext{max}} = 2\pi f A$$

Question 7

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 8

Which of the following statements about simple harmonic motion (SHM) is correct?

Accepted Answer

The frequency of SHM does not depend on the amplitude of oscillation.

Question 9

A mass oscillates on a spring with period $$T = 2.0\ 	ext{s}. If $$the amplitude is doubled, what is the new period?

Accepted Answer

$$2.0\ 	ext{s}$$

Question 10

A mass on a spring is released from rest at its maximum displacement $$A. At $$this instant, what are the values of its velocity and acceleration?

Accepted Answer

Velocity is zero; acceleration is maximum.

Question 11

A pendulum clock is designed so that one swing (back and forth) takes 2.00 s. What should be the length $$L of $$the pendulum? ($$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$L = 0.993\ 	ext{m}$$

Question 12

Which of the following best describes the energy transformation in a playground swing modeled as a pendulum?

Accepted Answer

Potential energy is maximum at the endpoints, and kinetic energy is maximum at the lowest point.

Question 13

A mass $$m$$ oscillates on a spring with spring constant $$k. $$What is the frequency $$f of $$the oscillation?

Accepted Answer

$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Question 14

A building sways in the wind with amplitude $$A = 0.40\ 	ext{m}$$ and period $$T = 7.7\ 	ext{s}. $$What is the maximum acceleration of the top of the building?

Accepted Answer

$$a_{	ext{max}} = (2\pi f)^2$ A$$

Question 15

Which of the following is a real-world example of simple harmonic motion?

Accepted Answer

The vibration of the membrane in the human ear due to sound waves.

Question 16

A pendulum and a mass-spring system both undergo simple harmonic motion. Which statement is true about their periods?

Accepted Answer

The period of a pendulum depends only on its length and $$g$$, while the period of a mass-spring system depends on the mass and spring constant.

Question 17

A mass oscillates on a spring. At what position is the kinetic energy of the mass at its maximum?

Accepted Answer

At the equilibrium position ($$x = 0).$$

Question 18

A pendulum is released from rest at a small angle. At which point is the restoring force greatest?

Accepted Answer

At the maximum displacement (endpoints).

Oscillations and Simple Harmonic Motion: Physics with Algebra Study Guide

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