Problem 3 Multi-DOF Response to a Cyclic Input (40pts) In the previous assignment, we modeled a passive quarter suspension model. Now we add a controller to make the suspesion system active. As shown. Mc 1 % c Suspension И kebc System +zw Zw Wheel & kw Tire Mw www bw Zr With me 1.0 Metric Tons, m = 20kg, be 1000N s/m, bw 900N s/m, ke 1500N/m, k = 2000N/m. a. (20%) Derive the equations of motion for the system. Then derive, symbolically, the transfer function relating the actuator input to car height: Ze(s) U(s)