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Hello and thanks for your question. My name is XXXXX XXXXX I will do all I can to help.
Let me first ask, do you feel it sitting at a light at idle? Or do you have to be moving down the road to feel this vibration in the gas pedal?
Alright, and you never noticed this before the differential repair correct?
Alright, I believe it's highly possible that the transmission or engine mounts were loosened when replacing the differential, and it's possible the engine/trans assembly isn't sitting neutralized in the frame, (in other words it was tightened down while in a slight bind) or the engine mount or transmission mount themselves are failing. Causing this vibration to be transferred from the powertrain into the body of the vehicle. It's also possible they could have loosened the exhaust system when performing the repair. If the exhaust system isn't installed neutrally, meaning bent slightly or in a bind when tightened back up, the exhaust can then transfer vibration through to the body, this is usually not as sever however, because the exhaust usually hangs from rubber mounts and you don't get as much transfer from the exhaust system.
Your vehicle doesn't have a mechanical throttle cable or linkage, so there isn't a direct connection to the engine as older vehicles had. I suspect the rear engine mount is either loose, in a bind, or failing then, as that would be the closest engine mount to the gas pedal hardware that attaches it to the body. Another thing that comes to mind, if you really notice it more on acceleration, or merging onto a highway, and not so much going downhills, It's possible it could be a CV joint. when they wear out, you can get that pulsating vibration feel in the body of the car, this is usually noticed in the steering wheel as well though on accell.
Yes, because that is the only place the engine or trans. can "transfer" the vibration to any other part of the vehicle. It sits on rubber mounts, (sometimes filled with hydraulic fluid) so if the rubber has torn, or the fluid has leaked out, that is what I suspect is the cause.
absolutely. Thank you.
Please let me know if you have any more questions.