Car Symptoms: The car vibrates when stopped.Possible Cause: The rear shoes and drums are misaligned.
Trouble shooting car vibration when stopped
Usually when the car vibrates when stopped it means that there is something wrong with the rear brakes. The reason is that the rear shoes of the drums are not even contact during brake application, when I say not even contact it means that the rear shoes and drums are misaligned and this will cause vibration.
Usually the reason for misalignment is that the rear drums are warped. But it is also possible that there is no problem with the drums but rather the rear wheel bearings is the problem. It is possible that the rear bearings are worn out or loose, if this is the case then it will cause an indirect misalignment between the brakes shoes and the drums.
See also: Car Vibrates at Certain Speeds
What to do?
Bring the car to a car shop then tell the mechanic to check the rear wheel bearings, ask the mechanic to look into the rear bearing if it is loose or worn out. If there is no problem with the bearings then the problem is the brake drums warpage. In this case you need to have the drums machined to correct warpage also after the drums are machined you need to replace the brake shoe because the old brake shoe will not have even contact with the newly machined brake drum.