Gas gauge jumps around when moving

I assume this is for a car.

The damping is a combination of the regulator and the gauge.

The gage is usually oil filled and slow responding, thus I would suspect that.

The regulator usually supplies a pulse. This minimizes power dissapation.

The float rarely is part of the damping system.

COPIED from Electrical Forum

This is likely a faulty instrument panel buffer that is built into the cluster.
I would check with your local GM dealer to inquire about program updates that may apply to your specific vehicle.