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Features of interaction of elements of a dynamic quencher of oscillations in the form of a rigid body with two degrees of freedom are considered. It is shown that the dynamic quencher is interpreted in structure of mechanical oscillatory system with object of protection as additional negative tie which can be presented by the generalized spring. Dynamic ruggedness of the generalized spring depends on the frequency of external indignation and defines manifestations of dynamic properties, characteristic for the modes of dynamic blanking out of oscillations. The generalized spring possesses properties of a quasi-spring that creates possibilities of various transformations of structure of system. Introduction of concept of the generalized transmission ratio of the lever ties arising between coordinates of the movement of elements of a dynamic quencher is offered. Forms of the transfer relations of lever ties are in univocity with system of the chosen coordinates. The transfer relations of lever ties allow to detail forms of mutual movements of elements of system. The method of creation of mathematical models is developed for an assessment of lever properties of movements of mechanical oscillatory systems.