#### Answer

4

#### Work Step by Step

The maximum height that the weight rises above the equilibrium position of $s(t)=0$ is the amplitude of the function. Therefore, we need to find the value of the amplitude.
To do this, we first write the equation in the form $y=c+a \cos [b(x-d)]$. Therefore, $y=-4\cos 8\pi t$ becomes $y=0-4\cos [8\pi(t-0)]$.
Comparing the two equations, $a=-4$. The amplitude is $|a|=|-4|=4$ inches.