Find the displacements \(x_{1}(t)\) and \(x_{2}(t)\) in Fig. 5.53 for \(m_{1}=1 \mathrm{~kg}, m_{2}=2 \mathrm{~kg}\), \(k_{1}=k_{2}=k_{3}=10,000 \mathrm{~N} / \mathrm{m}\), and \(c_{1}=c_{2}=c_{3}=2000 \mathrm{~N}-\mathrm{s} / \mathrm{m}\) using the initial conditions \(x_{1}(0)=0.2 \mathrm{~m}, x_{2}(0)=0.1 \mathrm{~m}\), and \(\dot{x}_{1}(0)=\dot{x}_{2}(0)=0\).

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000 k x(1) m2 x2(1) ell k3 FIGURE 5.53 Damped two-degree-of-freedom system.