Chapter 4.4, Problem 98E

a.

To determine

To find: the displacement when $t=0$

Answer to Problem 98E

  $\text{2 cm}$

Explanation of Solution

Given:

The displacement is given by,

  $y=2\cos 6t$

Substitute $t=0$ , in the expression $y=2\cos 6t$ .

  $\begin{array}{c}y\left(0\right)=2\cos \left(6\cdot 0\right)\\ =2\cos 0\\ =2\left(1\right)\\ =2\end{array}$

b.

To determine

To find: the displacement when $t=\frac{1}{4}$

Answer to Problem 98E

About $0.1414\text{ cm}$

Explanation of Solution

Given:

The displacement is given by,

  $y=2\cos 6t$

Substitute $t=\frac{1}{4}$ , in the expression $y=2\cos 6t$ .

  $\begin{array}{c}y\left(\frac{1}{4}\right)=2\cos \left(6\cdot \frac{1}{4}\right)\\ =3\cos \frac{3}{2}\\ \approx 2\left(0.0707\right)\\ \approx 0.1414\end{array}$

b.

To determine

To find: the displacement when $t=\frac{1}{2}$

Answer to Problem 98E

About $-1.997\text{ cm}$

Explanation of Solution

Given:

The displacement is given by,

  $y=2\cos 6t$

Substitute $t=\frac{1}{2}$ , in the expression $y=2\cos 6t$ .

  $\begin{array}{c}y\left(\frac{1}{2}\right)=2\cos \left(6\cdot \frac{1}{2}\right)\\ =2\cos 3\\ \approx 2\left(-0.998\right)\\ \approx -1.997\end{array}$