Abstract
The traditional calculation of mechanisms for forced harmonic oscillations is often a difficult task. Most often, calculators are interested in the steady-state modes of harmonic oscillations. The purpose of this paper is to significantly simplify calculations by replacing the need to solve differential equations with simpler algebraic methods. A complex representation of harmonic and related quantities is used. This approach is widely used in theoretical electrical engineering. Parallel and serial connections of mechanical power consumers are considered. The velocities of elements of mechanical systems and the forces applied to them are determined algebraically from the known parameters of systems and the disturbing harmonic effect. The use of a symbolic (complex) description of mechanical systems under forced harmonic vibrations (in steady-state mode) allowed us to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations, and replace it with simpler and more visual algebraic operations. Due to this, the time of calculations is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems under harmonic influences, have substantial methodological significance, since they show quantitative and phase relations between the parameters of systems.
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