### Oscillations

Let $y$ be the coordinate of the body. Then $F=-k\Delta l=-k(y-x)$. We have
$m\ddot{y}=-k(y-x)-b\dot{y}\Rightarrow m\ddot{y}+b\dot{y}+ky=kx_0\cos(\omega t)$
Therefore, $y=A\cos(\omega t-\phi)$. Substitute and complete.