Answer
$s(t)=2\cos 4\pi t$
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 $s(0)=2$. Since the function is cosine, this means that the amplitude is 2.
We also know that the period is 0.5 seconds. We can find the value of $w$ using the period through the formula:
Period$=\frac{2\pi}{w}$
$0.5=\frac{2\pi}{w}$
$w=\frac{2\pi}{0.5}$
$w=4\pi$
Substituting the values of $a$ and $w$, we find that the equation is:
$s(t)=2\cos 4\pi t$
