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Abstract. . The possibilities of changing the dynamic state of mechanical oscillatory systems are considered on the basis of using additional connections that are implemented by introducing lever mechanisms. Through the example of the problem of the dynamics of a solid body with two degrees of freedom and elastic supports, it is shown that the kinematic impact on the side of the bearing surface can be greatly reduced by a deliberate displacement of the concentrated masses on the elements of the lever device. The method for developing mathematical models is proposed. The results of the experiment are presented.Keywords: mechanical oscillatory systems, dynamic damping of vibrations, modes of simultaneous damping in two coordinates.