Pontiac Repair: 2003 Grand Prix 3.8L (2002 production date) unknown shake, grand prix 3, axle shaft

Question
2003 Grand Prix 3.8L (2002 production date foudn this out after replacing the thermostat)  I just bought my car new and it runs great, starts great.  Recently ive noticed when my car hits roughly 45-50mph the engine or something starts shaking.  I can feel it in the accelerator and the shaking comes and goes away again as i drive on the highway. I had my dad check it out and he said the most shaking is between 50-65mph.  The same thing happens in third gear but not as bad.  I took it back for my warrenty but they said all I need is a balance, but I can feel it in the accelerator, and its worse when i accelerate, and eases up a little when I ease up off of the gas.  I know this could be many things from emissions to transmission, but Do you have any ideas from the get go?  I ran some fuel injector cleaner through the system, and i have no check engine lights.  Thanks!

Answer
Hi David:

A vibartaion that is only there for a certain amount of road speed can be drive train related or wheel and ire related. the first thiugh would be a bad tire or wheel. If this car has good tires on it have the tires road force balanced not just spin balanced. It takes wheel run out and tire run out into consideration and balances them accordingly. It costs more than a regular spin balancing but it works. If it has questionable tires on it don't bother spending the money. It could be something like a loose motor mount or a motor mount that's grounding out You could have an axle shaft that has a cv joint that's starting to go bad but you would more than likely feel it in the steering wheel also. if you had a tire on the back of the car that was out you could feel it in the floor or the seat so they are not off base with that. if it's really a bother you can take it into the dealer and have them hook up a toold called the eva it is a vibartion analizer and after some simple math it can determine if it's a tire/wheel or drivetrain vibration it will not tell you exact what but at least it's not just a guess of a bad tire. good luck :}