A vibration damping device includes first and second accelerometers which are used to determine the relative displacement between a body and a base between which the device is operatively connected. The output of one of the accelerometers is also monitored in a manner to determine the frequency of the vibration. This data is processed in a manner to ascertain the timing when the phases of a vertical spring input (produced by the compression of an elastomeric member which defines the main spring of the damper) and an expansion spring input (produced the displacement of rheopetic fluid between first and second variable volume chamber and the associated expansion characeristics of the members defining the same) are reversed. Using this data and the vibration frequency data the timing with which a voltage should be applied to electrodes disposed in an orifice interposed between the first and second chambers to increase the viscosity of the rheopetic fluid and increase the flow resistance of the orifice. The device further includes a perforate suspended mass which is tuned in a manner to act as a dynamic damper.