Chapter 5.3, Problem 89E

Harmonic Motion A weight is oscillating on the end of a spring (see figure). The displacement from equilibrium of the weight relative to the point of equilibrium is given by

$y=\frac{1}{2}\left(\cos 8t-3\sin 8t\right)$

Where $y$ is the displacement (in meters) and $t$ is the time (in seconds).

Find the times when the weight is at the point of equilibrium $\left(y=0\right)$ for $0\le t\le 1.$