Consider a system subjected to two input forces, as shown in Figure 4.30. Find the transfer functions, \(X(s) / \mathcal{F}_{1}(s)\) and \(X(s) / \mathcal{F}_{2}(s)\). Find the response \(x(t)\) due to \(F_{1}(t)=t\) and \(F_{2}(t)=u(t)\). Use zero initial conditions, and let \(m=1 \mathrm{~kg}, k_{1}=500 \mathrm{~N} / \mathrm{m}\), and \(k_{2}=1000 \mathrm{~N} / \mathrm{m}\).

k x mo m F(1) k Figure 4.30: Two-input system. F(1)