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Hi I'm Brian and I'm here to help!
You're on the right track with the capacitor(s)! I would change it (them) as a matter of course since they're so cheap online. Let me know if you'd like help sourcing it (them). At the same time, you should carefully look at ALL wiring connections in the entire unit, including and especially the terminal connections at the compressor terminal box. You will have to remove the top on the ac unit to get to that. Tighten EVERYTHING! Just make sure you take note of the condenser fan wiring when you remove the top for re-installation. Also, you should check the high voltage connections in the safety disconnect switch that should be on the wall right next to the unit. Weak capacitors and loose wiring are the number one causes of this issue.
I should caution you, capacitors (especially blown ones) can hold a nasty charge even after the power is shut off to them. So with power shut off, you should take a screwdriver, and only holding the handle, short each capacitor terminal to the unit casing with the shaft of the screwdriver before touching them. This will ensure the capacitor is discharged and won't bite you!
Let me know if you have further questions on this subject. Otherwise, please remember to rate before leaving (3 stars or higher please!). Bonuses are always appreciated! Thanks for allowing me to help and thanks for using Just Answer!