This paper addresses the problem of obtaining robust and stable oscillations in a mechanical system. These oscillations are associated to a limit cycle that is born through a supercritical Hopf bifurcation. The method proposed in the paper works well for fully actuated systems, and even for certain underactuated ones. In order to illustrate the method, we have been chosen an underactuated system that is well known in the literature and in control systems laboratories: the inverted pendulum. Actual stable and robust oscillations have been obtained experimentally in a rotating Furuta pendulum.