The dc motor of Problem 11.1 has a field-winding inductance Lf = 3.7 H and a moment of inertia J = 0.081 kg · m2. The motor is operating at rated terminal voltage and an initial speed of 1300 r/min.

a. Calculate the initial field current If and duty cycle D. At time t = 0, the PWM duty cycle is suddenly switched from the value found in part (a) to D = 0.60.

b. Calculate the final values of the field current and motor speed after the transient has died out.

c. Write an expression for the field-current transient as a function of time.

d. Write a differential equation for the motor speed as a function of time during this transient.