Consider the system shown in Figure 4-64. The system is at restfor t < O. Assume that the displacement x is the output of thesystem and is measured from the equilibrium position. At t = 0, thecart is given initial conditions x(O) = Xo and x(O) = Vo' Obtainthe output motion x(t). Assume that m = 10 kg, bI = 50 N-s/m, b2 =70 N-s/m, k I = 400 N/m, and k2 = 600 N/m.

k D b X m k + b Figure 4-64 Mechanical system.