A pump is disclosed having a damped dynamic vibration absorber for attenuating pump vibration in response to a periodic disturbing force generated when the pump is in operation. The vibration absorber comprises elastic means, an annular mass and an energy dissipative means. The elastic means are arranged around the pump in a plane generally normal to the axis of rotation having one end secured to the pump and one end free to vibrate relative to the pump. The annular mass is secured to the free end and the energy dissipative means comprising a squeeze film damper is secured to the annular mass. The annular mass has a predetermined mass, and the elastic means have a predetermined stiffness and the squeeze film damper has a predetermined damping ratio such that the absorber generates a compensating force acting on the pump out of phase with a periodic disturbing force which acts on the pump and is generated while the pump is operated. The effect of the compensating force is to attenuate vibration of the pump which would otherwise occur as a result of the periodic disturbing force.