A slider-crank mechanism is used to impart motion to the base of a spring-mass-damper system, as shown in Fig. 4.38. Approximating the base motion \(y(t)\) as a series of harmonic functions, find the response of the mass for \(m=1 \mathrm{~kg}, c=10 \mathrm{~N}-\mathrm{s} / \mathrm{m}, k=100 \mathrm{~N} / \mathrm{m}\), \(r=10 \mathrm{~cm}, l=1 \mathrm{~m}\), and \(\omega=100 \mathrm{rad} / \mathrm{s}\).

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wt y(t) x(t) k/2 00000 m 00000 k/2 mu FIGURE 4.38 Input through slider crank mechanism