The simple pendulum motion by considering the mass of the string: Asymptotic corrections

In this paper the movement of a pendulum is analyzed considering the mass of the string from which the pendulum hangs, the analysis is carried out by perturbations considering that the mass of the string is much less than the mass of the pendulum. The results show that the mass of the string has two effects on the motion of the pendulum, the first is the increase in the inertia of the system and modification of the center of mass of the system, which translates into an increase in the frequency of the pendulum and the second effect is produced by the vibrations of the string itself, modifying the movement of the pendulum.