In Fig. $($D$),$ both $M^{\text{'}}$ s are equal with $M=0\mathrm{.}5kg*\frac{s^2}{m}$ each and they are connected rigidly. All the other components are the same as in $2($b$).$

a$)$ Derive the equation of motion for the system.

b$)$ Solve for the displacement of $M($connected to the spring$)$ for $f(t)=u(t).$ Note: Laplace of $u(t)=\frac{1}{s}$