Chapter 4.8, Problem 59E

To determine

To find: The maximum displacement of $d=4\cos 8\pi t$ .

Answer to Problem 59E

The maximum displacement is 4.

Explanation of Solution

Given Information:

The simple harmonic motion is described by the trigonometric function $d=4\cos 8\pi t$ .

The trigonometric function is $d=4\cos 8\pi t$ .

By comparing it with general harmonic equation $d=a\cos wt$

The maximum displacement is the amplitude $\left|a\right|=4$ .

To determine

To find: The frequency of the function $d=4\cos 8\pi t$ .

Answer to Problem 59E

The frequency of given function is 4.

Explanation of Solution

Given Information: The simple harmonic motion is described by the trigonometric function $d=4\cos 8\pi t$ .

The frequency is the reciprocal of the period; $\frac{w}{2\pi }=\frac{8\pi }{2\pi }=4\text{cycles}\text{per}\text{unit}\text{time}$ .

If the time is in seconds, then frequency = 4 Hertz.

To determine

To calculate: The value of $d$ when $t=5$ .

Answer to Problem 59E

The value of $d$ is 4.

Explanation of Solution

Given Information: The simple harmonic motion is described by the trigonometric function $d=4\cos 8\pi t$ .

Put in t = 5; then $d=4\cos \left[8\pi (5)\right]=4\cos 40\pi =4\cos 0=4$

For even multiple of p have reference angle 0°.

To determine

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

Answer to Problem 59E

The value of $t=0.0625$ .

Explanation of Solution

Given Information:

The simple harmonic motion described by the trigonometric function $d=4\cos 8\pi t$ .

The value of cos will be 0 if the angle = $\frac{\pi }{2}$ ,

  $\begin{array}{l}\frac{\pi }{2}=8\pi t\\ t=\frac{\pi }{2(8\pi )}=\frac{1}{16}\\ t=0.0625\end{array}$