At a certain speed meaning speed where vibration of the rear end occur, your car rear end vibrates but the front end does not.
Car Problem Diagnosis
When rear wheels are out of balance it will not rotate evenly making vibration occurrence on your car. You will notice this only at a certain speed where there is a severe vibration occurrence. Possible cause of this unbalance rear wheel is that the balancing weight that is positioned into your tire assembly may have been detached. As you may not aware during tire and rim assembly a balancing weight, usually led, is attached to the edge of the rim to compensate the unbalance that cause by not perfectly manufactured tire or rim. If the wheel weights is detached this can cause the wheels to vibrate on the portion where the wheel weights detached.
Possible Cause of Rear End Vibration at Certain Speed
Out of balance rear wheels.
How to Fix Rear End Vibration at Certain Speed
Bring your car to a reputable auto repair shop and have your tire balance. Two methods is used to balance the tire assembly, the first method is the static balancing where your tire assembly is removed in your car then put into balancing machine. The other method is the dynamic, where balancing is done while your tire is installed into your car, If you ask what type is the best, I would say it will be the dynamic balancing since it gives consideration on the influence of your car brake drums or brake disc during balancing.