Answer
$s(t)=-3\cos 2.5\pi t$
Work Step by Step
The equation of the function is $s(t)=a \cos wt$.
We know that $s(0)=-3$. A negative sign means that the object is pulled down at the start. Since the function is cosine, this means that $a=-3$.
We also know that the period is 0.8 seconds. We can find the value of $w$ using the period through the formula:
Period$=\frac{2\pi}{w}$
$0.8=\frac{2\pi}{w}$
$w=\frac{2\pi}{0.8}$
$w=2.5\pi$
Substituting the values of $a$ and $w$, we find that the equation is:
$s(t)=-3\cos 2.5\pi t$
