Shaking gimbal is obviously not normal. Does it do it inflight only or on startup as well?
If it's only doing it in flight it's possible one of the dampeners dislodged or is blocked by debris; you can open it up and have a look at the gimbal assembly and the attachment points (youtube away).
If it's doing it during startup you can try a gimbal calibration on a flat/level surface and see if that helps. If that doesn't help than you can try a factory reset using DJI Assistant 2 for Phantom but I wouldn't hold my breath at this point. It's quite likely that one (or more) of the gimbal motors and or ribbon cable / connectors are damaged and/or adrift.
If your phantom is less than 6 months old, the gimbal will be covered under warranty (provided you didn't crash the drone); Raise a support ticket with DJI and start the warranty process. They'll fix it or (more likely) replace your drone with a refurb.
If it's older than 6 months pay a visit to a local repair shop and have them diagnose it or try to fix it yourself.
Best of luck.