Title | On the question of studying forced vibrations of a linear system of two coupled oscillators near resonance |
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Authors | P. A. Shamanaev^{1}, D. A. Osipov^{1}^{1}National Research Mordovia State University |

Annotation | The article presents using of the Lyapunov-Schmidt method to study a mathematical model of vibrations in a system of two coupled oscillators near a resonance with a small parameter. It is assumed that an external periodic force with three comparable frequencies acts on the system. The algorithm developed on the basis of the Lyapunov-Schmidt method is implemented in the SymPy Python mathematical library. As an example, a certain system with fixed parameters is considered. A periodic solution is found for it, plots of the components of periodic solutions and phase trajectories are plotted. |

Keywords | coupled oscillators, forced vibrations, periodic solutions, small parameter, Lyapunov-Schmidt method, resonance |

Citation | Shamanaev P. A., Osipov D. A. ''On the question of studying forced vibrations of a linear system of two coupled oscillators near resonance'' [Electronic resource]. Proceedings of the XVI International scientific conference "Differential equations and their applications in mathematical modeling". (Saransk, July 17-20, 2023). Saransk: SVMO Publ, 2023. - pp. 256-261. Available at: https://conf.svmo.ru/files/2023/papers/paper41.pdf. - Date of access: 02.12.2023. |

**© SVMO, National Research Mordovia State University, 2023**

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