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Vibrations absorption in mechanical systems is a phenomenon which has been calling the attention of researches in the last decades. Its importance stems from the fact that is possible to suppress or attenuate undesirable vibrations on a mechanical system, when the system is in operation. Dynamic vibration absorbers have been studied in depth for mechanical systems of one degree freedom. In this work we investigate systems of two degrees of freedom that performs rotational and translational vibrations. The system is subjected to external harmonic perturbations. The inverted pendulum-absorber, integrated as a subsystem, has the ability to dissipate the mechanical energy coming from the main system or primary system, when the auto-resonance condition is tuned. The determination of the tuning condition for systems of several degrees of freedom is not a trivial task. In the present case there are three tuning conditions that are determined using the perturbation technique of the multiple scales method. Numerical simulations are presented as results of the analysis of the proposed mathematical model.