Find the free-vibration response of the spring-mass system shown in Fig. 6.32 for (m_{1}=m, m_{2}=2 m, m_{3}=m,

Question:

Find the free-vibration response of the spring-mass system shown in Fig. 6.32 for $m_{1}=m, m_{2}=2 m, m_{3}=m, k_{1}=k_{2}=k$, and $k_{3}=2 k$ corresponding to the initial conditions $\dot{x}_{3}(0)=\dot{x}_{30}$, and $x_{1}(0)=x_{2}(0)=x_{3}(0)=\dot{x}_{1}(0)=\dot{x}_{2}(0)=0$.

Figure 6.32:-