Answer
Period$=\frac{1}{4}$ seconds
frequency=4 oscillations per second
Work Step by Step
The period can be found by first comparing the equation $s(t)=-4\cos 8\pi t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity.
By comparing the two equations, we find that $w=8\pi$. Next, we find the period using the formula:
Period$=\frac{2\pi}{w}$
Period$=\frac{2\pi}{8\pi}$
Period$=\frac{1}{4}$ seconds.
Since frequency is the reciprocal of the period, it is 4 oscillations per second.
