Answer
(a) $4\ in$
(b) $\frac{1}{8}\ sec$
(c) $4\ Hz$ (cycles per second), $\frac{1}{4}=0.25\ sec$
Work Step by Step
Given the model equation $s(t)=-4\ cos(8\pi t)$, we have:
(a) the maximum height that the weight rises above the equilibrium position is the amplitude $|A|=|-4|=4\ in$
(b) Let $cos(8\pi t)=-1$, we have $8\pi t= \pi$ thus $t=\frac{1}{8}\ sec$ which gives the time when the weight first reach its maximum height.
(c) Use $\omega=2\pi f=8\pi$, we have $f=4\ Hz$ (cycles per second), the period is $p=\frac{1}{f}=\frac{1}{4}=0.25\ sec$
