Chapter 9.4, Problem 23E

To determine

To find: The period and the amplitude in the context of the situation.

Answer to Problem 23E

The period of the pendulum is $\frac{1}{4}$ and it shows the amount of time in second that the pendulum takes to go back and forth and return to the initial point, here the amplitude of 4 shows the maximum distances that the pendulum covers.

Explanation of Solution

Calculation:

Consider thegiven model for the motion of the pendulum is,

  $d=4\cos 8\pi t$

Consider the general form is,

  $y=4\cos \pi x$

Consider the formula to obtain the period is,

  $\begin{array}{l}\frac{2\pi }{b}=\frac{2\pi }{8\pi }\\ b=\frac{1}{4}\end{array}$

Then,

  $d=4\cos \frac{t}{2}$

Then, the graph for the above function is shown in Figure 1

  

Figure 1

The period of the pendulum is $\frac{1}{4}$ and it shows the amount of time in second that the pendulum takes to go back and forth and return to the initial point, here the amplitude of 4 shows the maximum distances that the pendulum covers.