#### Answer

4 inches

#### Work Step by Step

The maximum height that the weight rises above its equilibrium position is called the amplitude. It can be found by comparing the equation $s(t)=-4\cos 10t$ to $s(t)=a\cos w t$ where $|a|$ is the amplitude.
Comparing the two equations, we find that $a=-4$. Therefore, the maximum height that the weight rises above its equilibrium position (amplitude) is:
$|a|=|-4|=4$ inches