Just bought a 2005 PT Crusier Touring Edition, need help pls.?

I bought this 2005 PT Cruiser Touring Edition about 2 weeks ago. It was a fairly good deal, only had 37,000 miles. When I was at the dealership everything seemed to check out. It drove smoothly, I had someone check the mechanics for me and everything looked good, I even took it overnight to really check everything out and I was happy with everything. Well last week I noticed that the car seems to be idling really rough. When I first start the engine it will be ok but after a minute or two the entire car seems to start shaking! (I know it's strange but the car seems to almost be shaking to a beat.. like a ...

whomp...whomp...whomp...whomp...whomp type of rhythm and not just a general shake, if that makes any sense) The steering wheel and seats shake, and you can even see the beam from the headlights moving up and down. The shaking only lasts for a few minutes and then goes away. It will run smoothly for awhile and then if I stop at a red light or something it will start shaking again for a moment, and then go away again. Well now I'm also noticeing that sometimes when I accelerate the shaking will start a little bit and then it almost seems like the engine wants to cut off briefly, it kinda.... gives a little kick (the only way I can think to explain it...it kinda seems to hesitate for a second) but then after that the car accelerates with no problem. The engine light is NOT on, and the shaking and hesitance only happen once in a while, they are not constant. I'm really kind of frustrated now. I took the car back to the dealership because I do have a 90 day warranty, but they said that they couldn't find anything wrong with it. I'm really upset and worried about this now, because it's still occuring sporatically. Does anyone have any idea what may be wrong with the car?? Thanks!