In order to improve servo system stability and decrease settling times in rotary head positioners for high performance magnetic disc drives, a floating mass damper is mounted on the end of an accessing head arm structure of the positioner opposite to the end or ends carrying the magnetic head or heads. The damper includes a spring centered floating mass which rests on a viscous film, such as silicone oil, and the shear forces developed by motion of the floating mass across the film dissipates vibrational mode energy in the accessing head arm structure during both a fast seek operation followed by track following fine servo operation. Such energy dissipation thus reduces the settling time and amplitude of natural resonance of the head positioner.