k b 772 "1 m www k Figure 1 Figure 2 2. (30 points) The mechanical system shown in Figure 2 has m = 20 kg, b = 180 N-s/m, and k = 1620 N/m. (a) Find the transfer function *(s) and determine the damping ratio < and U(s) natural frequency w of the system. (b) The system is at rest initially and then set into motion at t = 0 by an impulsive force of magnitude 90 N, that is u = 90 8(t). Obtain the motion x(t) and the velocity of the mass immediately after the impulsive force is applied.