Problem 4 The mechanical system is shown in Fig. 4. Assume that the input and output are the displacements u(t) and y(t), respectively. The displacement y(t) is measured from the equilibrium position. Sup- pose that u(t) = sin wt. What is the output y(t) at steady state? Plot the response y(t) and find the magnitude (in dB) and phase angle (in degrees) for w = 6.97137 rad. Draw Bode plots for the system. Assume that the system is linear throughout the operating period and m = 1kg, b = 1.5244 Ns, and k = 9.29516 N. Answer: L(w)= m' sec m. ww y(t) u(t) m k O b Figure 4: Mechanical system in Problem 4 dB x(w)= °