Find the response of the system shown in Fig. 5.66 with \(m_{1}=2, m_{2}=1, k_{1}=40\), and \(k_{2}=20\) for the following initial conditions using Laplace transform:

i. \(x_{1}(0)=0.05, x_{2}(0)=0.10, \dot{x}_{1}(0)=0, \dot{x}_{2}(0)=0\)

ii. \(x_{1}(0)=0.10, x_{2}(0)=-0.05, \dot{x}_{1}(0)=0, \dot{x}_{2}(0)=0\)

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m = 1 kg 0000 k = 20 N/m m =2 kg k = 40 N/m FIGURE 5.66 Undamped two-degree-of-freedom system.