Time-harmonic motion of a mechanical system consisting of a water layer and a freely floating body (either surface-piercing or totally submerged) is studied. It is proved that the total energy of the water motion is finite and the equipartition of the energy of the whole system is established. Under certain restrictions on the geometry of the body, the problem is proved to have only a trivial solution for sufficiently large values of the frequency. The lower limit of the uniqueness frequencies are estimated.
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