Find the free-vibration response of the two-degree-of-freedom system shown in Fig. 5.6 with \(n=1, k=8\), and \(m=2\) for the initial conditions \(x_{1}(0)=1, x_{2}(0)=\dot{x}_{1}(0)=0\), and \(\dot{x}_{2}(0)=1\).

Figure 5.6:-

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T x (1) "wwwww k = k m = m 00000 k = nk m = m X(1) k3 = k FIGURE 5.6 Two-degree- of-freedom system.