Complex concepts for calculation of mechanical systems in harmonic processes

It is noted that the traditional calculation of mechanisms for forced vibrations is often a difficult task. Most often, calculators are interested in steady-state modes of oscillation. The aim of the work is to significantly simplify calculations by replacing the need to solve differential equations with algebraic methods. This approach is widely used in electrical engineering. The use of a symbolic (complex) description of mechanical systems with forced harmonic oscillations (in a steady state) made it possible to abandon the extremely cumbersome and laborious calculation algorithm associated with solving differential equations and replace it with simple and visual algebraic operations. Thanks to this, the calculation time is reduced significantly. Vector diagrams, while not being a necessary component of the study of mechanical systems, have significant methodological significance, since they show quantitative and phase relationships between the parameters of systems.