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This article discusses an electromechanical system in the form of an electrodynamic loudspeaker. To describe the dynamics of a loudspeaker, a finite-dimensional model with a given number of a finite number of independent mechanical and electrical parameters is used. Using the electromechanical analogy force - voltage and using the Lagrange-Maxwell equations, a closed system of two nonlinear differential equations of the second order of motion of the system is compiled. Using modern advances in computer technology, a number of numerical experiments were performed in the Mathcad system with varying values of the input parameters of the system, such as the mass of the moving coil, inductance, ohmic resistance, and graphs of the time variation of the coil movement and current strength were plotted. Phase portraits were also built. The movement of the system has the character of damped oscillations, and the phase portraits have a stable focus. The influence of the varied parameters on the period of damped oscillations and the transition of the system to the state of equilibrium is shown. The study was carried out for a nonlinear model without the use of asymptotic methods, which made it possible to exclude the methodological error of the solution. The model can exhibit complex dynamics. Having a mathematical model and a calculation program, it is possible to carry out further studies of the system under consideration, identifying the positions of stable and unstable equilibrium, modes of self-oscillations, defining areas of periodic and chaotic modes of different nature. The results obtained can be used in the development of technical devices capable of demonstrating complex behavior. Methodologically, the proposed material is interesting for undergraduate and graduate students specializing in electromechanics, in terms of teaching the principles of constructing and analyzing electromechanical systems. |
