Answer
$s(t)=5\cos\frac{4\pi}{3} t$
Work Step by Step
The equation of the function is $s(t)=a \cos wt$ where $a$ represents the amplitude and $w$ represents the angular speed.
We know that $s(0)=5$. Since the function is cosine, this means that the amplitude is 5.
We also know that the period is 1.5 seconds. We can find the value of $w$ using the period through the formula:
Period$=\frac{2\pi}{w}$
$1.5=\frac{2\pi}{w}$
$w=\frac{2\pi}{1.5}$
$w=\frac{4\pi}{3}$
Substituting the values of $a$ and $w$, we find that the equation is:
$s(t)=5\cos\frac{4\pi}{3} t$
