Chapter 9.4, Problem 24E

To determine

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

Answer to Problem 24E

The period of 6 shows the amount of time in seconds that the buoy takes to go back and forth to the same position. Here, the amplitude 1.75 represents the maximum distance in feet of the bob from the sea level. The graph of the model is shown in Figure 1

Explanation of Solution

Given:

The given model for the vertical displacement of the boy is of the form $y=1.75\cos \frac{\pi }{3}t$ .

Calculation:

Consider the given model for vertical displacement of the boy is,

  $y=1.75\cos \frac{\pi }{3}t$

Consider the general form is,

  $y=a\cos bx$

Consider the formula to obtain the period is,

  $\begin{array}{l}\frac{2\pi }{b}=\frac{2\pi }{\frac{\pi }{3}}\\ b=6\end{array}$

Then,

  $y=1.75\cos 6t$

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

  

Figure 1

The period of 6 shows the amount of time in seconds that the buoy takes to go back and forth to the same position. Here, the amplitude 1.75 represents the maximum distance in feet of the bob from the sea level.