Answer
The weight first reaches its maximum height at $t = 0.125~seconds$
Work Step by Step
$s(t) = -4~cos~8\pi~t$
The weight reaches its maximum height when $cos~8\pi~t = -1$.
We can find $t$ when the weight first reaches its maximum height:
$cos~8\pi~t = -1$
$8\pi~t = \pi$
$t = \frac{1}{8} = 0.125~s$
The weight first reaches its maximum height at $t = 0.125~seconds$
