Shaking from the rear

I have a weird shake coming from the rear of my car.

This only occurs when accelerating from a stop, and causes the car to shake violently until I hit about twenty km/h, after which, the car operates as normal. Here are some clues I have gathered:

-Occurs only when accelerating from a stop (longer and more pronounced when accelerating slowly).

-No noise is heard past twenty to thirty km/h.

-No noise is heard if you allow the car to move forward without stepping on the gas.

-Occurs regardless of what gear you accelerate from stop with (first, second, third, can be selected through gear knob).

-Occurs during turning as well.

-Causes the car to shake, and not accelerate as normal.

-Traction light comes on during the rumble.

-A pump can be heard from the engine bay.