Chapter 6.6, Problem 8E

(a)

To determine

To find: The highest point reached by the knot.

Answer to Problem 8E

The amplitude of the model is $0.5$ .

Explanation of Solution

Given information:

The given function is $h=-3\cos \left(\frac{5\pi }{3}t\right)+3.5$

Calculation:

Calculate the highest point reached by the knot.

  $3+3.5=6.5$

Therefore, the highest point reached by the knot is $6.5$ .

(b)

To determine

To find: The lowest point reached by the knot.

Answer to Problem 8E

The lowest point reached by the knot is $0.5$ .

Explanation of Solution

Given information:

The given function is $h=-3\cos \left(\frac{5\pi }{3}t\right)+3.5$

Calculation:

Calculate the lowest point reached by the knot.

  $-3+3.5=0.5$

Therefore, the lowest point reached by the knot is $0.5$ .

(c)

To determine

To find: The period of the model.

Answer to Problem 8E

The period of the model is $3$ .

Explanation of Solution

Given information:

The given function is $h=-3\cos \left(\frac{5\pi }{3}t\right)+3.5$

Calculation:

Calculate the function

  $2$ pi divided by $5pi$ over $3$ .

Therefore, the period of the model is $3$ .

(d)

To determine

To find: The highest of the knot after $25\sec ond$ .

Answer to Problem 8E

The highest of the knot after $25\sec ond$ is $2$ .

Explanation of Solution

Given information:

The given function is $h=-3\cos \left(\frac{5\pi }{3}t\right)+3.5$

Calculation:

Calculate the highest of the knot after $25\text{second}$

  $\begin{array}{c}h=-3\cos \left(\frac{5\pi }{3\times 25}\right)+3.5\\ \cos \left(\frac{5\pi }{3\times 25}\right)=0.5\\ -3+0.5=-1.5\\ -1.5+3.5=2\end{array}$

Therefore, the highest of the knot after $25\sec ond$ is $2$ .