when parked in drive, you can feel a rough vibration, heard and felt mostly near the back of the car, this vibration goes away once the car is being driven
My car has 138000 miles.
My car has an automatic transmission.
Hello - I would be suspicious of an exhaust system hanger which has gone weak, and is allowing the exhaust to bump into the chassis at an idle. It is also possible that the fuel pump is wearing out, and the "chattering" that a worn fuel pump makes is transmitted through the fuel tank into the car. It would be easier to notice at a stoplight, but fades while driving as other road noise increases. I recommend a vibration and noise inspection performed by a mobile, professional mechanic, such as one from YourMechanic, who will come to your location, diagnose this problem, and give you an accurate assessment of damage and cost estimate for repairs.
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