Determine the response of the system of Figure 6.7 due to a force \(F(t)=\) \(40 \sin 60 t \mathrm{~N}\) applied to the block whose displacement is \(x_{1}\) using the method of undetermined coefficients. Use \(m=20 \mathrm{~kg}, k=200,000 \mathrm{~N} / \mathrm{m}\), and \(c=400 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}\).

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x2 k FIGURE P6.7 m 2m