We're going to need some more details if you want good answers. All engines "vibrate". It's a matter of how you define it. I'm thinking it must have been really bad for the engine to be replaced under warranty. Now it's doing the same thing? Maybe you could get some video of it.
My 07 auto just starting do this as well. Cold start, in gear and feeling like a dead cylinder. Just barely touch the gas, it vibrates right through the steering wheel and can even feel it on the floor. Once under way, no vibration. more noticeable when the engine is cold, less when hot.
broken, damaged flex plate/flywheel is the most common.. tensioner bad, accessory pulley bad or accessory bad..
Pilot bearing (manual trans) bad..
Transmission input shaft bearings shot..
that will keep you busy for a while.. surprised that chrysler replaced a motor without doing due diligence to make sure what was wrong especially since it was under warranty..
if the do warranty work and it does not fix the problem they dont get paid..
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