The approximation methods to investigate the dynamical processes in the strong nonlinear single-or multi-degree physical systems are studied in the paper. The developed procedure of the investigation of the oscillations in the nonlinear systems with the concentrated mass can solve not only the analysis problems but the problems of the cyberphysical oscillation system synthesis on the projective phase choosing such system characteristics enabled the resonance phenomena as well. There is described the real application of the obtained results to analyze the technical systems using to protect the equipment from the vibration load.