Torsional vibration of a complex electro-mechanical system consisting of a VFD controller and AC induction motor is investigated in this thesis to study the dynamical behavior of a rather complex motor drive, used to power a DC generator and a set of heat-generation resistors for achieving various levels of nominal loads over a wide range of nominal frequencies/speeds. Two magnetic encoders are placed at two locations to record the arrival times of two arrays of teeth in connection with a data acquisition system. Through a Matlab-coded algorithm, the instantaneous angular speeds and their harmonic compositions up to 16th order of the mean motor speed can be accurately discerned. The model and the algorithms developed in this thesis can be used in a variety of machines and testing systems powered by induction motors and regulated by variable-frequency-drive controllers for design, condition monitoring and identification of sources of noise and disastrous vibration.