Chapter 4.8, Problem 63E

To determine

To find: The maximum displacement of function $d=\frac{1}{16}\sin 140\pi t$ .

Answer to Problem 63E

The maximum displacement of function is $\frac{1}{16}$ .

Explanation of Solution

Given Information: It is given that the simple harmonic motion is described by the trigonometric function $d=\frac{1}{16}\sin 140\pi t$ .

The given trigonometric equation is $d=\frac{1}{16}\sin 140\pi t$ , compare it with $d=a\sin wt$ . The maximum displacement is the amplitude $\left|a\right|=\frac{1}{16}=00625$ .

To determine

To find: The frequency of function $d=\frac{1}{16}\sin 140\pi t$ .

Answer to Problem 63E

The frequency of the function is 70.

Explanation of Solution

Given Information: It is given that the simple harmonic motion is described by the trigonometric function $d=\frac{1}{16}\sin 140\pi t$ .

The given trigonometric equation is $d=\frac{1}{16}\sin 140\pi t$ , compare it with $d=a\sin wt$ . The frequency is reciprocal of the period $\frac{w}{2\pi }=\frac{140\pi }{2\pi }=70$ cycle per unit of time.

If the time is in seconds, then frequency = 70 hertz.

To determine

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

Answer to Problem 63E

The value of d for the given values is 0.

Explanation of Solution

Given Information: It is given that the simple harmonic motion is described by the trigonometric function $d=\frac{1}{16}\sin 140\pi t$ .

The given trigonometric equation is $d=\frac{1}{16}\sin 140\pi t$ , compare it with $d=a\sin wt$ . Put t = 5

  $\begin{array}{l}d=\frac{1}{16}\sin [140\pi (5)]\\ =\frac{1}{16}\sin [700\pi ]=0\end{array}$

Even multiple $\pi$ have reference angle 0.

To determine

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

Answer to Problem 63E

The least positive value of t is $\frac{1}{140}$ .

Explanation of Solution

Given Information: It is given that the simple harmonic motion is described by the trigonometric function $d=\frac{1}{16}\sin 140\pi t$ .

The given trigonometric equation is $d=\frac{1}{16}\sin 140\pi t$ , compare it with $d=a\sin wt$ . The sin will be 0 if the angle is $\pi$ , why not 0 because they want the least positive value so that t > 0.

You can count 7 cycles from 0 to 0.1, so from t = 0 and t = 1 there will be 70 cycle.