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Hello, on that motor the two browns (one brown and one brown and white stripe) go the *run capacitor... you buy that separately for the specific motor.
*do not use the wire that used to connect to the 'fan' terminal on the units dual capacitor... you will no longer use that side of the existing dual capacitor in this case.
The other two wires (not the browns) go directly to t1 and t2 on the contactor... but only IF this is not a heat pump.
except that it sounds like you are now using the original capacitor, and very often the capacitance is not sufficient for replacement motors, you should also check the amperage to make sure that your new motor is running at the correct amps and keep an eye on it to insure that is not running too hot,
If it is running high amps or hot, follow my original directions on how to wire it.
Stay in touch as needed,