Answer
$ d=-6 \cos \dfrac{\pi}{2} t $
Work Step by Step
Amplitude, $|A|=-6$
Given: $ Period =4$ and $ f=\dfrac{\omega}{2 \pi}$
Now, period, $ P=\dfrac{2 \pi}{\omega} \implies \omega =\dfrac{2 \pi}{4}=\dfrac{\pi}{2}$
So, $ d=A \cos \omega t=-6 \cos \dfrac{\pi}{2} t $
Hence, $ d=-6 \cos \dfrac{\pi}{2} t $
