This method uses a sum of weighted acceleration signals to experimentally predict the external force which excites a mechanical system. The method is shown to yield excellent results in experiments conducted on a mass-loaded, free-free, steel beam. Random vibration was used to excite the beam in preliminary tests conducted to determine the optimal distribution of the weighting factors which can be associated with an equivalent mass at each accelerometer location. The system dynamic degrees of freedom (reflecting an upper frequency limit) are directly related to the number of independent acceleration measurements. Follow-on experiments demonstrate how the technique can be used to correctly predict an unknown force-time signature. Alternate techniques for determining the weighting factors are discussed. The technique does not appear to be overly sensitive to variations in the mass matrix.