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According to the present invention, a tuneable inertia damper for suppressing vibrations in a machine tool is proposed which allows independently controlling the stiffness and the damping, for adapting to the vibration frequency of the structure to dampen during the machining process, such that high precision machining both in dimensions and in surface finish is achieved. The main objective is to improve productivity since when the stability of the cutting process increases greater pass depths, and therefore removing material more quickly, are allowed. The second advantage is greater precision.