Comportamiento asintótico para el periodo del péndulo simple

Abstract

We investigate the asymptotic behaviors of the period for a simple pendulum with arbitrary initial conditions. The study of the vibrational and rotational solutions for the simple pendulum shows that in the asymptotic limit the behavior is of the same type for both motions, when the energy tends to $mgl$. Here we present a logical deduction for the behavior in both cases. We obtain that the asymptotic behavior of the period goes to infinity logarithmically for the two solutions of the pendulum.