## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$- 4 \ \sin( 4t)$
The object starts at the vertical position $y=0$, and moves in the downward direction. The frequency is given by: $\omega=\dfrac{2\pi}{T}$ So, the function has the form $y=-a \ \sin(\omega t)=-a \ \sin(\dfrac{2\pi}{T} t)$. Here, $y=- 4 \times \sin (\dfrac{2\pi}{\frac{\pi}{2}} \times t)= - 4 \ \sin( 4t)$