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Control of oscillations in mechanical systems in the start-up and passage through resonance modes is studied. In both cases, the control algorithm is based on the speed-gradient method with energy-based goal functions. It is shown that for Hamiltonian 1-degree of freedom (DOF) systems, it is generically possible to move the system from any initial state to any final state by means of a controlling force of arbitrarily small intensity. Controlled passage through resonance is studied for a 5-DOF vibration machine taking friction into account. It is shown by simulation that applying feedback control makes passage through lower resonance feasible with smaller control intensity compared with passage through resonance under constant control torque. The specific feature of this paper is consideration of the case when constant control torques do not allow the rotors even to start rotation. Applying feedback control allows rotors to overcome gravity and to start rotation. Another key novelty of this paper is comparison of the results obtained from the simulation with the experimental results obtained from the two-rotor laboratory mechatronic stand. It appears that most results are qualitatively the same, which confirms the adequacy of the model.