This paper has studied the identification problem of linear mechanical systems where inputs are unknown and only displacement data are accessible for measurement. Eigensystem Realization Algorithm (ERA) has been used along with physical constraints considerations in time domain to simultaneously identify two separate models for the physical system and the unknown inputs. Inputs are assumed to be an arbitrary combination of harmonic signals with frequencies higher than natural frequencies of the physical system by which a linear mechanical system is meant in this paper. Adding physical constraints and utilizing canonical real Jordan form of the identified system leads to a unique analytical solution. To validate the theory part, a set of simulations has been run that demonstrates the physical parameters and input model can be estimated accurately.

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