This paper analytically investigates expressions of an oscillating motor's air-gap torque resulting simultaneously from dynamic electromagnetic and dynamic mechanical components. The electromagnetic torque is generated in the air gap when the motor is supplied by variable frequency drives (VFDs), such as pulsewidth modulated voltage source inverters or load commutated inverters. Whereas, the mechanical torque components might result from dynamic mechanical processes, such as wind turbine blades, oil and gas fluid fluctuation, and, for emulating dynamic mechanical loads, a load-side VFD. Simple and straightforward analytical relationships between electrical and mechanical harmonics are developed to understand the propagation of mechanical dynamics to the electric side and vice versa. Intensive numerical simulations have been carried out to support the theoretical analysis. Time and frequency domain results confirm the robustness of the proposed relationships. Finally, laboratory experimental test results also confirm the accuracy of the proposed relationships.