fixed magnetic field brushed DC motor is used to control a pendulum, idealized as a uniform rod of length and mass m. The motor torque T, is proportional to the armature current i, by a constant factor K, known as the motor torque constant (T = K i). The back emf, is proportional to the angular velocity of the motor shaft, by the constant K as well. Assuming that the source voltage is the manipulated variable (control input), Kirchoff's voltage law the first ODE describing the behavior of the electrical circuit is