[inverter]

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

 

[piotrsko]

If it's a polarized cap there will be markings for positive (but not sure which way that goes) I usually run non polarized. RUT 100mfd per hp original motor rating.

 

[kennybobby]

That white wire from the motor is the neutral return, it should be connected to the white wire of the AC input terminal (not to the chassis of your dismantled opener). Disconnect the red/white wire nut and connect the white from the motor with the white AC input wire. Disconnect the red wire from the capacitor and set it aside.

The blue wire from the motor goes to the blue on the capacitor, that blue capacitor terminal correctly goes to the black line from the AC input terminal.

The red from motor goes to the capacitor as it is already, the other red wire (disconnected as above) is extra you don't need it or connect it to anything, take it off the capacitor.

If you plugged it in as shown in your post, you likely blew the wall outlet breaker since the capacitor was connected shorted across the AC mains.

good luck and be safe,