Find the free-vibration response of the system shown in Fig. 5.5 (a) using Laplace transform approach for

Question:

Find the free-vibration response of the system shown in Fig. 5.5 (a) using Laplace transform approach for the following data: $m_{1}=2, m_{2}=4, k_{1}=8, k_{2}=4, k_{3}=0, c_{1}=0, c_{2}=0$, $c_{3}=0$. Assume the initial conditions as $x_{1}(0)=1, x_{2}(0)=0$, and $\dot{x}_{1}(0)=\dot{x}_{2}(0)=0$. Plot the responses $x_{1}(t)$ and $x_{2}(t)$.

Figure 5.5(a):-