Determine the free response of the system of Figure P6.8 if the machine tool has initial velocities of \(\dot{x}(0)=0.8 \mathrm{~m} / \mathrm{s}\) and \(\dot{\theta}(0)=5 \mathrm{rad} / \mathrm{s}\). if \(I=0.03 \mathrm{~kg} \cdot \mathrm{m}^{2}\), \(c=100 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}, m=3 \mathrm{~kg}, a=0.3 \mathrm{~m}, b=0.4 \mathrm{~m}\) and \(k=3000 \mathrm{~N} / \mathrm{m}\).

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G m, I X x1 C k k FIGURE P6.8