Using the formulation of continuum mechanics, a dynamic reciprocal theorem is derived for sinusoidal motion of an elastic medium. It is found that, exactly as in the static case, the work of the forces of State 1 acting through the displacements of State 2, equals the work of the forces of State 2 acting through the displacements of State 1. A simple example is given, which illustrates the application of the reciprocal theorem to the analysis of forced vibrations of beams.

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