Two 1-DOF pendulums coupled with a weak spring are considered. This system is a coupled Controlled Hamiltonian Systems that has been studied widely in these days. The control objective is to make pendulums swing synchronously with small input. To this end, Speed Gradient Energy method proposed by Fradkov is adopted to design the controller. Although experimental results showed that the method succeeded in achieving the objective, the mechanism of synchronization was not clear. In this study, the contracted dynamics of the whole system is analyzed and properties of the system are investigated. Through the investigation, a criteria to define the feedback gain of the controller is revealed. Computer simulation and experimental results showed the validity of the method.