A wound DC motor is connected in both a shunt and a series configuration. Assume generic resistance and inductance parameters Ra, Rf, La, Lf, let the field magnetization constant be kf and the armature constant be ka. Assume ideal energy conversion, so that ka kT. The motor has inertia Jm and damping coefficient bm, and it is rigidly connected to an inertial load with inertia J and damping coefficient b. a. Sketch a system-level diagram of the two configurations that illustrates both the mechanical and electrical systems. b. Write an expression for the torque-speed curve of the motor in each configuration. c. Write the differential equations of the motor-load system in each configuration. d. Determine whether the differential equations of each system are linear; if one (or both) is (are) nonlinear, could they be made linear with some simple assumption? Explain clearly under what conditions this would be the case.