A periodic force \(F(t)=A \cos \omega t\) is applied to the damped system shown in Figure 3.53. Calculate the work done in one cycle during the steady-state response where \(A=50 \mathrm{~N}, \omega=10 \mathrm{rad} / \mathrm{s}, k=6 \mathrm{kN} / \mathrm{m}\), \(c=200 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), and \(m=25 \mathrm{~kg}\).

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-0000- k m Figure 3.53: Mass suspended between a spring and a damper.