This research investigates the behavior of a three-phase induction motor with a squirrel cage rotor under various eccentricity conditions. A mathematical model is developed to simulate the rotor's oscillatory motion, incorporating both mass eccentricity and magnetic forces. The model is then used to analyze the motor's vibrations in both time and frequency domains. Results show that static eccentricity causes vibrations at twice the electrical frequency, while dynamic eccentricity leads to a rotor frequency signal modulated by a lower frequency related to rotor precession. The developed model can be applied for diagnosing rotor eccentricity issues in induction motors.