College Physics: Reasoning and Relationships

Nicholas J. Giordano

Chapter 11

Harmonic Motion and Elasticity - all with Video Answers

Educators

Section 1

General Features of Harmonic Motion

Problem 1

A simple harmonic oscillator takes 15 seconds to undergo 25 complete oscillations.
a. What is the period of the oscillator?
b. What is the frequency of the oscillator?

Km Neeraj

Km Neeraj

Numerade Educator

Problem 2

A person's heart beats 70 times in 1 minute. What is the average frequency of this oscillation?

Km Neeraj

Numerade Educator

Problem 3

Figure P11.3 shows the displacement of a simple harmonic oscillator as a function of time.
a. Find the period, frequency, and amplitude of the oscillator.
b. At what time(s) does the acceleration have its largest positive value?
c. When does the acceleration have its most negative value?

Km Neeraj

Numerade Educator

Problem 4

Figure P11.4 shows a plot of the position as a function of time for a particle undergoing simple harmonic motion. Identify the following points on this graph: a. Where is the speed largest?
b. Where is the velocity positive with its magnitude being largest?
c. Where is the magnitude of the acceleration largest?
d. Where is the force on the particle zero?

Km Neeraj

Numerade Educator

Problem 5

a. For the simple harmonic oscillator in Figure $\mathrm{P} 11.3$, estimate the velocity at $t=4.0 \mathrm{s}$ and at 7.0 s.
b. At what time $(s)$ does the velocity have its largest positive value?

Km Neeraj

Numerade Educator

Problem 6

The displacement of a harmonic oscillator is given by $y=3.4 \sin (25 t),$ where the units of $y$ are meters and $t$ is measured in seconds. Find
a. the amplitude and
b. the frequency.

Km Neeraj

Numerade Educator

Problem 7

The displacement of a harmonic oscillator is given by $y=9.4 \sin (15 t),$ where the units of $y$ are
meters and $t$ is measured in seconds. What is its maximum velocity?

Km Neeraj

Numerade Educator

Problem 8

The displacement of a harmonic oscillator is given by $y=7.1 \sin (48 t),$ where the units of $y$ are meters and $t$ is measured in seconds. Give three values of $t$ at which the oscillator has
a. its largest (and positive) displacement and
b. its largest (and positive) velocity.

Km Neeraj

Numerade Educator

Problem 9

Figure P11.9 shows the velocity as a function of time for an oscillator. Is it a simple harmonic oscillator? Explain why or why not. What is its frequency?

Km Neeraj

Numerade Educator

Problem 10

A simple harmonic oscillator has a frequency of $300 \mathrm{Hz}$ and an amplitude of $0.10 \mathrm{m}$. What is the maximum velocity of the oscillator?

Km Neeraj

Numerade Educator

Problem 11

Figure $\mathrm{P} 11.11$ shows the velocity of a simple harmonic oscillator as a function of time.
a. Estimate the position when $v=0$
b. Estimate the frequency.

Km Neeraj

Numerade Educator