hi billy a single phase ac induction motor is made up of two phases internally so its really a 2 phase induction motor , the capacitor is used to generate the 2nd phase to give a set rotation and also starting torq.
the single phase comes in and is directly wired to the run coil of the motor the second coil is run with the capacitor in place and the capacitor creates a phase lag so the second coil gets a sine wave that lags in time to the run coil so now it runs as there are two phases rotating, its hard to convert these to run on a 2 phase inverter however as youl usually find the start winding and run windings will have different inductances
the single phase comes in and is directly wired to the run coil of the motor the second coil is run with the capacitor in place and the capacitor creates a phase lag so the second coil gets a sine wave that lags in time to the run coil so now it runs as there are two phases rotating, its hard to convert these to run on a 2 phase inverter however as youl usually find the start winding and run windings will have different inductances