Determine the response of the system of Figure P6.8 due to a unit impulse applied at the mass center. Use \(m=100 \mathrm{~kg}, I=4.5 \mathrm{~kg} \cdot \mathrm{m}^{2}, k=200,000 \mathrm{~N} / \mathrm{m}\), \(c=500 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}, b=2 \mathrm{~m}\), and \(a=1 \mathrm{~m}\).

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b +a G x2 m, I 1x x1 FIGURE P6.8 k