Gas and Oil Home Heating Furnaces - HVAC Condenser Fan Motor

I am trying to replace a Condenser Fan Motor on my Central Air Conditioning unit. The old motor has 3 wire leads blcak, yellow and brown. The Central Air unit has a dual function capacitor with 3 posts. The new motor has 4 wire leads black, purple, brown and brown with a white stripe and I purchased a new capacitor with 2 posts rated at 3mfd to match the new motor.
I am not able to get the motor run because I do not know how to connect the wires to the capacitor.

Any suggestions?

The black wire will connect where the old motor black wire connected. The purple wire goes where the yellow wire connected. The post on the original capacitor where the brown wire was will be EMPTY.

The 2 brown wires connect to two posts of the new capacitor. That's it.