Software for research oscillation process in the system of oscillators with different masses

• Published in: Ukrainian journal of educational studies and information technology 2019-12, Vol.7 (4), p.10-23
• Main Authors: Yeremieiev, Volodymyr, Briantsev, Oleksandr, Naumuk, Oleksii, Samoilov, Volodymyr
• Format: Article
• Language: English
• Subjects: mathematical model; oscillators; oscillatory process; software
• ISSN: 2521-1234; 2521-1234
• DOI: 10.32919/uesit.2019.04.02

A mathematical model is formulated as a system of differential equations for the analysis of the oscillatory process in linear oscillators with different masses. It is assumed that the left end of the first oscillator is fixed and an arbitrary force is attached to the last oscillator. The algorithm for solving the problem using the Euler and Runge-Kutta numerical methods is proposed. Two Euler and RungK applications have been developed for calculations. The program code is compiled in the C++ algorithmic language in Microsoft Visual Studio 2012. The accuracy of the calculated data depends on the number of oscillators and the time of oscillation. Testing showed that in the case of one or two oscillators, the program RungK, based on the Runge-Kutta method, provides 10-10% accuracy of calculations. The error of the calculated parameters is almost independent of the number of time intervals from 103 to 106. The accuracy of the Euler method, which is implemented in Euler, is about 0.5% under similar conditions. Increasing the number of iterations to 104, 105, and 106 leads to the increase in accuracy to 0.05%, 0.005%, and 0.0005%, respectively. The software can be useful in the analysis of oscillatory processes in a linear oscillate ditch.