Vibration of a rotor-bearing system driven by an electric motor is a coupled phenomenon between mechanical characteristics and magnetic origins through the air-gap. With the advent of new high-energy magnets together with high precision motor applications, magnetic sources of vibration are becoming more serious. This paper investigates the transient whirl responses of a rotor system with purely mechanical origins and compares it with that of magnetically coupled origins. A perturbation method is applied to model the magnetic field associated with rotor eccentricity. Electromagnetic forces are obtained by the Maxwell stress method, which utilizes the analytical expression of radial flux density distribution. The FEM was applied to a rotor-motor system to illustrate magnetically coupled effects in rotor dynamics. Results show that magnetically coupled sources significantly affect the vibration of the rotor-motor system.