I one had a furnace vibrate very much and it almost shook the trailer. And this is the rest of the story.
This is how I found out that a "Mud Dabber" got into my combustion fan through the combustion air intake. How I found out was that one morning I heard the furnace going 'hum/click" repeatedly, and it would not come on. Found out that fan would not turn, so I took furnace apart and found that the mud dabber nest had come loose from the fan blade and jammed the fan. Actually there is one motor on with a double shaft that works both fans. Got the nest out and could not believer how much quitter furnace as. After that I put some aluminum screen over the intake and outlets of the furnace.
You could have a similar problem with a nest in your AC unit.