Abstract
Period-3 oscillations of pendulum are investigated using the method developed in our previous paper [1]. Values of the driving force within very narrow ranges may give rise to this kind of motion. Because of the extreme sensitivity of the equation to the force strength and initial conditions, some features of the system can hardly be depicted, either numerically or experimentally. However, by analytically obtaining a map of states it is possible to detect the underlying structure of the system of solutions. The theory predicts the existence of unstable periodic solutions. Also, it predicts stable period-3 solutions around the top position of pendulum. Trajectories obtained by numerically integrating the pendulum equation in a phase-locked condition agree with our diagrams.
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