What is the role of capacitors in washing machines?

Update:06 Mar 2020
Summary:

For single-phase motors to achieve forward and reverse […]

For single-phase motors to achieve forward and reverse rotation, the main and auxiliary windings need to lead out two wires respectively.
A total of four lineswall fan motor Manufacturers in China
Assume that the head of the main winding is A and the tail is B; the head of the secondary winding is X and the tail is Y.
When A and X are connected to the common terminal and connected to the power supply L, then Y is connected to the capacitor, the other end of the capacitor is connected to B, and connected to the O terminal of the power supply. The motor is in a direction of rotation.
When A and Y are connected to the common terminal and connected to the power supply L, then X is connected to the capacitor, the other end of the capacitor is connected to B, and connected to the O terminal of the power supply, the motor is in another direction of rotation.
The capacitor acts to advance the phase of the series winding by an angle to facilitate the motor start