Answer
$ - 4 \ \sin( 4t)$
Work Step by Step
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,
$y=- 4 \times \sin (\dfrac{2\pi}{\frac{\pi}{2}} \times t)= - 4 \ \sin( 4t)$
