Chapter 9.4, Problem 68E

(a)

To determine

To find:The displacement, period of the spring and then graph the function.

Answer to Problem 68E

The graph of the function is shown in Figure (1), its amplitude is $1$ and period is $\frac{\pi }{3}$ .

Explanation of Solution

The motion of spring is modelled by,

  $y=0.2\cos 6t$

The graph of the above function is shown below.

  

Figure (1)

From the graph the period is = $\frac{\pi }{3}$ .

The amplitude is $1$ .

Therefore, the graph of the function is shown in Figure (1), its amplitude is $1$ and period is $\frac{\pi }{3}$ .

(b)

To determine

To graph: The function and its effect on motion.

Answer to Problem 68E

The graph of the function is show in Figure (2) and its amplitude is reduced to zero.

Explanation of Solution

The motion of spring is modelled by,

  $y=0.2e^{-4.5t}\cos 4t$

The graph of the above function is shown below.

  

Figure (1)

The amplitude is reduced to zero.

Therefore, the graph of the function is show in Figure (2)and its amplitude is reduced to zero.