Derive expressions for the Laplace transform of (x_{1}(t)) and (x_{2}(t)) for the system shown in Fig. 5.5

Question:

Derive expressions for the Laplace transform of $x_{1}(t)$ and $x_{2}(t)$ for the system shown in Fig. 5.5 (a) for the following data: $m_{1}=1, m_{2}=2, k_{1}=4, k_{2}=2, k_{3}=0, c_{1}=1, c_{2}=2$, $c_{3}=0, f_{1}(t)=F_{0} u(t)=$ step function, and $f_{2}(t)=0$. Assume the initial conditions of both $x_{1}(t)$ and $x_{2}(t)$ as zero.

Figure 5.5(a):-