Answer
$y =- 10 \ \sin( \dfrac{2\pi t}{3})$
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 (simple harmonic motion):
$y=-a \ \sin(\omega t)=-a \ \sin(\dfrac{2\pi}{T} t)$.
Here,
$y=-10 \times \sin (\dfrac{2\pi}{3} \times t)=- 10 \ \sin( \dfrac{2\pi t}{3})$
