Why does a synchronous motor need extra windings to start?

A synchronous motor is not self-starting because, at any speed other than synchronous speed, the rotor experiences an oscillating torque with a zero average value as the stator's rotating magnetic field repeatedly passes the slower-moving rotor.1

To overcome this, a short-circuited winding—often called a damper winding—is added to the rotor. This winding functions similarly to that of an induction machine to provide the necessary starting torque. The motor is brought up to approximately 95 percent of its synchronous speed using this winding, at which point the direct current field is applied, allowing the rotor to pull into synchronism with the revolving field.1

Beyond facilitating the start, these windings serve a secondary purpose: they dampen oscillations caused by sudden load changes while the motor is in synchronism, as any deviation in speed induces currents in the damper windings that produce a counteracting torque.1