Answer
$ d=-8 \cos \pi t $
Work Step by Step
Amplitude, $ A=-8$
(negative because the object is moving down initially.)
Given: $ Period =2$
Now, period, $ P=\dfrac{2 \pi}{\omega} \implies \omega =\dfrac{2 \pi}{2}=\pi $
So, $ d=A \cos \omega t=-8 \cos \pi t $
