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In this paper the existence of periodic orbits for a strongly non linear problem is rigorously proved. The non perturbed part of the system involves a cubic polynomial. In order to approach such problem is necessary to use elliptic functions. For non ideal problems this the first time that such kind of result is obtained.doi:10.5540/03.2017.005.01.0038 fatcat:ipcsimv2j5dxphzolsulnjnutq