An inverse method for the assignment of natural frequencies and nodes of normal modes of vibration by the addition of grounded springs and conentrated masses is presented. The method relies entirely on measured receptances at the coordinates of the nodes and the modifications. Measurements at other locations are not needed, neither is there any need for an analytical model. The stiffness and mass parameters are determined by an analysis of the null space of a matrix containing the measured receptances. Example problems are used to illustrate the application of the technique.