(Solved): Consider a spring-mass-damper system shown below, where the input U(t) is displacement input and X ( ...

(a) (10pts) Derive the governing equations of motion of the system. (b) (5pts) Find the transfer function $\frac{X(s)}{U(s)}$ given the system parameter values of ${\mathbf{m}}_1={\mathbf{m}}_2=1,{\mathbf{c}}_1={\mathbf{c}}_2=1$, and ${\mathbf{k}}_1={\mathbf{k}}_2={\mathbf{k}}_3=1$. (c) (extra 5pts) Find the poles of the system in (b) and give a qualitative description of the motion in time domain when unit impulse input of $U$ is applied.