First check the belt tension. Best is with a tension gauge, but a Helm manual says how much the belt should move when you push it with your finger. Tell us what year & someone will probably come up with that info.

Too tight can give too much wear on bearings, too loose will let the belt flap & vibrate as it's spinning. But neither one seems like it would shake the car. So I'm gonna guess a pulley that's out-of-round.

Start the car, let it idle, turn on the A/C. Watch the A/C belt, and look carefully at each of it's pulleys. None of them should wobble as they spin. Wait for the compressor clutch to engage, sometimes that makes the wobbling worse. Find the bent one, & replace it.

Belts are easy to replace. How old are they? If the crank pulley is bent, that's a little harder. Compressor clutch or something like that should be harder, but I haven't had to do that (yet).