= 1. A DC motor is used to drive a I system includes two gear trains (to modify the applied torque and speed) and viscous damping of Cl = 36 Nm-s/rad and c = 8 Nm-s/rad as shown. The number of teeth on gear 1 is N 10, gear 2 is N2 = 20, gear 3 is 3 = 10, and gear 4 is N = 20. The torque-speed curve for the motor is shown in Figure 2. Assume that the inertial of the motor, Im, is negligible when compared to the other components of the system. 18 kg-m2 load as shown in the schematic. The = (a) Derive the differential equation that models the angular displacement of the load, (t) as a function of input motor voltage, v (t). (b) Derive the differential equation that models the angular velocity of the load, w(t) as a function of input motor voltage, v(t). + Gear 1 v(t) Motor Im 7 [Nm] Tstall = 5 Gear 2 C Gear 3 Toi Gear 4 Figure 1: Schematic of the DC motor driven system. w [RPM] Wno-load 600/ Figure 2: Torque-speed curve for the DC Motor when a 10 V input is applied.