Answer
$y=-10\cdot \cos\left(\frac{2\pi{t}}{3}\right)$
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: $y=-a\cdot \cos(\omega t)=-a\cdot \cos\left(\frac{2\pi}{T} \cdot t\right)$.
Here $y=-a\cdot \cos\left(\frac{2\pi}{T}\cdot t\right)=-10\cdot \cos\left(\frac{2\pi{t}}{3}\right)$.