2. Consider the system shown in Figure 2. An armature-controlled DC servomotor drives a load consisting of the moment of inertia JL. The torque developed by the motor is 7. The moment of inertia of the motor rotor is Jm. The angular displacements of the motor rotor and the load element are 8 and 0, respectively. The gear ratio is n=n/n. Assume the motor torque constant is K, the back emf constant is Kb. Derive the governing equations of this system. Obtain the transfer function between the output and the input voltage e,, i.e. 0(s)/E,(s). L R www Ө T JL In the figure, R armature resistance, 2; Figure 2. Armature-controlled DC servomotor system. T-torque developed by the motor, N-m Larmature inductance, H i armature current, A; JL Jm moment of inertia of the motor rotor, kg-m² moment of inertia of the load, kg-m² e, applied armature voltage, V e-backemf, V Om angular displacement of the motor rotor, rad angular displacement of the load element, rad n, number of teeth of gear 1 n, number of teeth of gear 2 i, magnetic field current, A. Assume the magnetic field is constant. 1