Hi,
I had a very similar problem in my sunfire. It actually turned out to be a loose muffler.
This is a common problem with sunfire's. What ends up happening is a small metal clip that connects the muffler to the frame of the car ends up breaking.
To check if this is the problem, make sure the car has had sufficient time to cool, and then grab the rear exhaust and see if it moves freely up and down (it should not move at all).
If it moves you can buy the part from any dealership and they can tell you where it goes (very hard to describe via chat).
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Tuesday, April 10th, 2012 AT 1:49 AM