In a previous work the second author presented a theory for the identification of a single-degree-of-freedom machine from its forced periodic operating characteristics. In this work that concept is extended by presenting two new methods of solution which, unlike the previous work, do not use Fourier series. The first method is a deterministic method of solution which is not restricted to using periodic data. This deterministic method is used to establish necessary and sufficient conditions for the existence of a unique solution. In particular, it is shown that three observations of the instantaneous drive shaft speed and torque characteristics under different operating conditions are necessary and that the observed speeds must satisfy two conditions. These conditions assure that the observations are independent of each other and that the observations uniquely define three periodic functions which characterize a machine belonging to the specified class of machines. The second method of solution is a least squares formulation which is derived from the first method; however, the derivation of this second method requires that the data be periodic.

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