The paper deals with the problem of controlling the pendulum mechanisms. To describe the dynamics of controllable systems, the Hamiltonian formalism is used. An algorithm is proposed for achieving equal energy values by means of feedback control based on the Speed-gradient method. The conditions of attainability of the control goal are obtained. A relation is established between the energy synchronization and oscillation frequency. The results of the computer simulations are presented showing achievement of the control goal and demonstrating the dynamical properties of the closed-loop system.