المجلة الدولية للعلوم والتقنية

The response of a dynamical non-linear system of two-degree-of freedom, is investigated. Analysis of the amplitude and phase plane is obtained. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to second order approximation. All possible resonance cases at this approximation are obtained and studied numerically to determine the worst case. The effects of different parameters are studied. The frequency response equations are solved numerically. These vibrations were controlled using the damper Keywords: Resonance; vibration control; Frequency response function; Multiple time Scale.