Diagnosis
This is a classic sign of a worn-out or unbalanced brush head. The internal motor is fine, but the attachment is causing the violent shaking.
How to Fix It
First, try a brand new, genuine AquaSonic replacement brush head. Make sure it clicks firmly into place. Turn it on. If it's smooth and quiet, the old head was the problem. If it's still rough with a new head, there's likely debris stuck in the mechanism.
If That Didn't Work
With the brush head removed, turn the handle on for a few seconds. Listen and feel. If it's still unusually loud and rough by itself, the motor's internal bearings or the drive shaft could be damaged from being dropped. That's an internal repair job.
Heads Up
Don't press down hard while brushing. Let the sonic vibrations do the work. Pushing the bristles flat against your teeth puts a huge lateral strain on the motor and shaft, wearing it out faster and making it noisier.