Vehicle vibrates/shakes only from the rear, no noises or other vibrations.

What is your question?

When I get up to around 35 MPH / 55 Kmh I start to feel vibrations (more like shaking) coming from the rear half of the car. I can see my rear window vibrating from the rear-view mirror. It does not go away at higher speeds however the shaking frequency increases so it actually becomes a bit less noticeable but still there. I don't feel any vibrations coming from the front or in the steering wheel, but I can feel it in my seat as a result of the rear half vibrating. No noises of any kind. Car has only 37k miles on it! I just bought the car used with no history so I'm worried. What could it be?

What makes this problem better or worse?

gets worse around 60-70 Mph

How long has your 2004 BMW 330Ci had this problem?

Just bought the car, so right away