The correct answer is: A. supplied with unbalanced voltage.
A 3-phase synchronous motor has three windings, each of which is connected to a different phase of the power supply. The windings are arranged so that the magnetic fields produced by each winding are in phase with each other. This creates a rotating magnetic field that causes the rotor of the motor to turn.
If the motor is supplied with unbalanced voltage, the magnetic fields produced by the windings will be out of phase with each other. This can cause the motor to vibrate and overheat. In severe cases, it can also cause the motor to stall.
Option B is incorrect because an under-loaded motor will not have enough current to produce a strong magnetic field. This will not cause the motor to vibrate or overheat.
Option C is incorrect because an over-loaded motor will have too much current. This can cause the motor to overheat, but it will not cause the motor to vibrate.
Option D is incorrect because the negative phase sequence is caused by unbalanced voltage.