Investigation of Forced Oscillations of a Linear System of Two Coupled Oscillators with a Small Parameter

The article is devoted to the description of the development of an algorithm for finding periodic solutions of one linear system of two coupled oscillators with a small parameter based on the Lyapunov-Schmidt method. The cases when the frequency of forced oscillations coincides with one of the natural oscillation frequencies are considered. Graphs of periodic solutions and phase trajectories of a system of two coupled oscillators have been constructed.