Answer
$y=-4\sin(4t)$
Work Step by Step
The object starts at the vertical position $y=0$, and moves down. By definition, the frequency is $\omega=\frac{2\pi}{T}$, hence the function is: $y=-a\cdot sin(\omega t)=-a\cdot sin(\frac{2\pi}{T} t)$.
Here, we have
$y=-a\cdot \sin\left(\frac{2\pi}{T} \cdot t\right)\\
y=-4\cdot \sin\left(\frac{2\pi}{\frac{\pi}{2}} \cdot {t}\right)\\
y=-4 \cdot \sin{\left(2\pi \cdot \frac{2}{\pi}\cdot t\right)}\\
y=-4\sin(4t)$.