Gidday there Zed,
Welcome to ECN, mate!. [Linked Image]
A capacitor-start motor, doesn't actually create a "second phase".
What happens, is the capacitor causes the usually lagging current of the start winding, to be shifted by 30 degrees, to bring it more into line with unity power factor.
Upshot of this, is that the start winding provides more useful power (having a higher power factor), through a lower current draw, during the starting phase.
Basically the capacitor takes the inductive component out of the windings of the motor.
Hope this helps.
If not, feel free to ask any other questions you may have.
Mike.