Find the response of the mass shown in Fig. 4.56 under the force \(F(t)=F_{0} e^{-t}\) using convolution integral. Data: \(k_{1}=1000 \mathrm{~N} / \mathrm{m}, k_{2}=500 \mathrm{~N} / \mathrm{m}, r=5 \mathrm{~cm}, m=10 \mathrm{~kg}, J_{0}=1 \mathrm{~kg}-\mathrm{m}^{2}\), \(F_{0}=50 \mathrm{~N}\).

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Pulley, mass moment of inertia Jo k 00000 2r Foe m T 00000 k1 x(t) FIGURE 4.56 Pulley-mass-spring system subjected to force.