Problem $2(8$ points$)$

Consider the system shown. The disk rolls with slipping $(2$ DOF$),$ when $$ and $x$ are zero, the spring is unstretched. The spring is fixed to center point of the disk C when the system is in equilibrium, and the disk rolls back and forth in small angles about this position. Determine the equations of motion for $$ and $x$ in matrices form

using complete FBD and Newton's laws.

using energy method.

$J_c=m\frac{R^2}{2}$