Vibration in a drill string is damped with a damping system coupled to the drill string. The damping system includes a chamber, a gas and piston in the chamber, and a mass connected to the piston. The gas defines a spring having a spring coefficient that is dependent on a volume or temperature of the chamber. The damping system is tunable in real-time by varying the volume or temperature of the chamber. In alternatives with multiple chambers interconnected to one another via ports, chamber volume at the existing pressure can be varied by selective actuation of valves between the chambers or the pressure of the gas can be varied by compressing or expanding a connected bellows or by heating or cooling the temperature of the gas. The damping system can selectively damp both radial and torsional vibrations.