A Tuned Mass Damper (TMD) for damping oscillations of a hanging vertical pump structure includes a removable mass symmetrically configured within the pump structure diameter and supported by a mechanism which provides damped mobility relative to the pump structure so as to absorb and dampen pump vibrations and oscillations. The TMD mass is easily removable before tipping of the pump between horizontal and vertical orientations during maintenance. In some embodiments, the TMD mass comprises fluid pumped by the pump to fully or partially fill a housing, the fluid being gravitationally drained therefrom when the pump is not operating. In other embodiments the TMD mass is supplied by removable solid weights. Damped mobility is provided by springs damped by mechanical or fluid friction, or by obstructed movement of fluid within a partially filled housing. In embodiments, the TMD mass is at least 5% of the total mass of the pump structure.