Here are the most common causes:
Driveshaft imbalances: If the driveshaft is not properly balanced, it can cause vibrations. This can be caused by a bent driveshaft, a damaged driveshaft joint, or a worn driveshaft bearing.
Bent axles: A bent axle can also cause vibrations. This can be caused by hitting a curb or pothole, or by an accident.
Faulty driveshaft: If the driveshaft joints are worn or damaged, it can also cause vibrations.
Worn bearings: Worn bearings in the differential can also cause vibrations.
Incorrectly set up pinion-gear and ring-gear backlash.
To determine the exact cause of the vibrations in the rear differential, you should have a qualified mechanic inspect the vehicle and check for these potential causes.