Chapter 4.8, Problem 64E

a.

To determine

To find: The maximum displacement of function $d=\frac{1}{64}\sin 792\pi t$ .

Answer to Problem 64E

The maximum displacement of the function is $\frac{1}{64}$ .

Explanation of Solution

Given Information: It is given that the simpler harmonic motion is described by the trigonometric function $d=\frac{1}{64}\sin 792\pi t$ .

The given trigonometric equation is $d=\frac{1}{64}\sin 792\pi t$ , compare it with $d=a\sin wt$ . The maximum displacement is the amplitude $\left|a\right|=\frac{1}{64}=0.01562$ .

b.

To determine

To find: The frequency of function $d=\frac{1}{64}\sin 792\pi t$ .

Answer to Problem 64E

The value of frequency is 396.

Explanation of Solution

Given Information: It is given that the simpler harmonic motion is described by the trigonometric function $d=\frac{1}{64}\sin 792\pi t$ .

The given trigonometric equation is $d=\frac{1}{64}\sin 792\pi t$ , compare it with $d=a\sin wt$ . The frequency is the reciprocal of the period $\frac{w}{2\pi }=\frac{792\pi }{2\pi }=396$ cycle per 1 unit of time. If the time is in seconds, then frequency will be 396 Hertz.

c.

To determine

To find: The value of d when t = 5.

Answer to Problem 64E

The value of d will be 0 for t = 5.

Explanation of Solution

Given Information: It is given that the simpler harmonic motion is described by the trigonometric function $d=\frac{1}{64}\sin 792\pi t$ .

The given trigonometric equation is $d=\frac{1}{64}\sin 792\pi t$ , compare it with $d=a\sin wt$ . Put t = 5

  $\begin{array}{l}d=\frac{1}{64}[\sin 792\pi (5)]\\ =\frac{1}{64}[\sin 3960\pi ]=0\end{array}$

Even multiple $\pi$ have reference angle 0.

d.

To determine

To find: The least positive value of t for which d = 0

Answer to Problem 64E

The least positive value of t will be $\frac{1}{792}$ .

Explanation of Solution

Given Information: It is given that the simpler harmonic motion is described by the trigonometric function $d=\frac{1}{64}\sin 792\pi t$ .

The given trigonometric equation is $d=\frac{1}{64}\sin 792\pi t$ , compare it with $d=a\sin wt$ . The sin will be 0 if the angle = $\pi$ , why not 0 because they want the least positive value so that t > 0.

  $\begin{array}{l}792\pi t=\pi \\ t=\frac{\pi }{792\pi }=\frac{1}{792}\\ =0.0012626\end{array}$