Engine idle issues

I have an 2002 Eclipse GS. When I first drive my car, even after warming it up and I stop at a light I can feel the engine shaking, a very noticeable shaking and I am pretty sure I can hear the exhaust pipe shaking as well. This persists until I get my car to above 40 mph and then the shaking stops for the rest of the day, until my car has sat for a while in which it does it all over again. It is not the engine or the transmission mounts because I just changed them. I just replaced the spark plugs and wires, pcv valve, even flushed the fuel injection system and I still have not figured out what the issue is. My check engine light has not come on or anything. Does anyone know what could be causing this issue?