A didactic exposition of the Runge-Kutta method in the study of the damped pendulum

Various natural phenomena are often modeled using differential equations. However, an analytical solution of such equations is not always possible, so numerical methods must be part of the physicists’ arsenal to study their system of interest. In this work we hope to provide a pedagogical presentation for projects that need to find solutions to ordinary differential equations using numerical methods. For this, we use the fourth-order Runge-Kutta method to describe the simple pendulum with the presence of a resistive force through its phase diagrams in subcritical, critical and supercritical damping, finally we compare the numerical solutions with the analytical results.

Keywords:
Numerical methods; Runge-Kutta; Damped pendulum