Answer
$x(t) = (8.0~cm)~cos(\pi~t+\pi)$
Work Step by Step
The general equation for the position of an object in SHM is:
$x(t) = A~cos(2\pi~f~t+\phi_0)$
It is known that:
A = 8.0 cm
f = 0.5 Hz
At $t = 0$, the object has its most negative position. This shows that the basic cos-curve is shifted an angle of $\pi$ to the left. Therefore, $\phi_0 = \pi$.
We can write the function for this motion as:
$x(t) = (8.0~cm)~cos[(2\pi)(0.5)~t+\pi]$
$x(t) = (8.0~cm)~cos(\pi~t+\pi)$
