The oscillations in a synchronous motor can be damped out by

maintaining constant excitation
running the motor on leading power factors
providing damper bars in the rotor pole faces
oscillations cannot be damped

The correct answer is: C. providing damper bars in the rotor pole faces.

Dampers bars are a type of winding that is placed in the rotor of a synchronous motor. They help to reduce the oscillations of the motor by providing a path for current to flow when the motor is not synchronized with the power grid. This current helps to stabilize the motor and prevent it from oscillating.

Option A is incorrect because maintaining constant excitation will not help to damp out the oscillations of the motor. In fact, it may actually make the oscillations worse.

Option B is incorrect because running the motor on leading power factors will not help to damp out the oscillations of the motor. In fact, it may actually make the oscillations worse.

Option D is incorrect because oscillations can be damped out by providing damper bars in the rotor pole faces.