I. Introduction

        Through a simple example, one will study the resonance problem in mechanics. A dynamical system, which can be mechanical, electrical or magnetical, is considered as resonant when it's able to modify its equilibrium state and to accumulate energy under the effect ofan external force. The resonance phenomenon appears when the frequency of  the force correspond with a particular frequency of the system: the resonance frequency of the system.

        When a dynamical system is subjected to a resonance phenomenon, it begins to oscillate and it can have a lot of vibrations. So, it can be very dammageable for the system and it is in some cases very important to avoid these phenomena.

        In this report, one will study the example of two pendulums linked with a spring. This system is subjected to a exciting force, which is periodic. One will see how does the system react, in function of the frequency of the force. This will allow us to see the impact of the resonance on a mechanical system.