## Precalculus (10th Edition)

$y=-6\sin(2t)$.
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: $y=-a\cdot \sin(\omega t)=-a\cdot \sin\left(\frac{2\pi}{T} \cdot t\right)$. Here, we have $y=-a\cdot \sin\left(\frac{2\pi}{T} \cdot t\right)=-6\cdot \sin\left(\frac{2\pi}{\pi} \cdot t\right)=-6\sin(2t)$.