Chapter 5.6, Problem 3E

(a)

To determine

To find: The amplitude, period, and frequency of the motion.

Answer to Problem 3E

The amplitude, period, and frequency of the motion is $2$ , $\frac{2\pi }{3}$ , and $\frac{3}{2\pi }\text{Hz}$ .

Explanation of Solution

Given Information:

The function model displacement of an object is,

  $y=2\sin 3t$

Concept used:

The standard form of the simple harmonic motion is given by,

  $y=A\sin \omega t$

The angular velocity is given by:

  $\omega =\frac{2\pi }{T}$

The function of the simple harmonic motion in time period term is given by,

  $y=A\sin \left(\frac{2\pi t}{T}\right)$

The function of the simple harmonic motion is givenby,

  $y=A\sin \left(\frac{2\pi t}{T}\right)$

The function model displacement of an object is,

  $y=2\sin 3t$

Compare both the equation to obtain,

  $\begin{array}{l}A=2\\ \frac{2\pi }{T}=3\\ T=\frac{2\pi }{3}\end{array}$

The frequency of the motion is calculated as,

  $\begin{array}{c}f=\frac{1}{T}\\ =\frac{3}{2\pi }\text{Hz}\end{array}$

Thus, the amplitude, period, and frequency of the motionis $2$ , $\frac{2\pi }{3}$ , and $\frac{3}{2\pi }\text{Hz}$ .

(b)

To determine

To find: The sketch of the motion.

Explanation of Solution

Given Information:

The function model displacement of an object is,

  $y=2\sin 3t$

The function model displacement of an object is,

  $y=2\sin 3t$

Consider the following graph of the displacement of the object over one complete cycle,