Answer
$y=-5\cdot \cos(\pi t)$.
Work Step by Step
The object start at the vertical position $y=-a$, and moves up. By definition, the frequency is $\omega=\frac{2\pi}{T}$, hence the function is: $y=-a\cdot \cos(\omega t)=-a\cdot \cos(\frac{2\pi}{T} t)$.
Here $y=-a\cdot \cos\left(\frac{2\pi}{T}\cdot t\right)=-5\cdot \cos\left(\frac{2\pi}{2} \cdot t\right)=-5\cdot \cos(\pi t)$.
