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Method of construction of mathematical models is offered for mechanical systems with additional feedback ties which formed of lever mechanisms of different kinds. It shown that mathematical models can be get by simplifying more complicated system in which lever ties are realized of rigid body with fixed pivot point. Lever ties at the preparation of a model formally appear at decrease inertial moment of intermediate rigid body to very small values. It shown that mechanical oscillation system can be reduced to equivalent scheme which matches estimation scheme of chain type. Equivalent estimation schemes can to differ of various kinds of between-partial ties. Possibilities of using quasi-springs in equivalent estimation schemes are offered and justified. These complicated compositions consist of elastical elements which interconnected of lever mechanisms. Coerced stiffness’s of quasi-springs defined on rules of transformation of structural mathematical models. Base of mathematical modeling is using method of transformation of Laplas with following construction of equivalent in dynamical attitude of structural schemes of automation control systems. Analytical ratios are given. They characterize possibilities of special dynamical regimes.

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.