Answer
$s(t)=-4\cos\frac{5\pi}{3}t$
Work Step by Step
The equation of the function is $s(t)=a \cos wt$.
We know that $s(0)=-4$. A negative sign means that the object is pulled down at the start. Since the function is cosine, this means that $a=-4$.
We also know that the period is 1.2 seconds. We can find the value of $w$ using the period through the formula:
Period$=\frac{2\pi}{w}$
$1.2=\frac{2\pi}{w}$
$w=\frac{2\pi}{1.2}$
$w=\frac{5\pi}{3}$
Substituting the values of $a$ and $w$, we find that the equation is:
$s(t)=-4\cos\frac{5\pi}{3}t$
