A Study of Super Nonlinear Motion of a Simple Pendulum and its Generalization

Two identically charged simple pendulums are dropped symmetrically about their common pivot in a vertical plane. For a set of parameters associated with each pendulum namely {mass,charge, and length} we evaluate the critical angle at which the forces acting on each pendulum are null resulting a static equilibrium. We then consider two dynamic non-equilibrium cases. In the absence of friction we analyze the features of steady oscillations of the pendulums resulting from setting the initial swing angles larger and then smaller than the critical angle. In each case, for a set of initial angles we evaluate the optimum separation angles of the charges and their corresponding acquired traversed times. For a comprehensive visual understanding we utilize Mathematica animation and display the features of the oscillations.