COMPUTATIONAL DESCRIPTION OF THE SIMPLE HARMONIC OSCILLATOR AND THE SIMPLE PENDULUM

A comparison between the equations of motion and periods of a simple pendulum and a simple harmonic oscillator was made using a computational technique. The equation of motion of the simple pendulum was determined using Lagrange’s equation of motion, and Mathematica 12.3 software was adopted to obtain the solution and period of oscillation. The equation of motion of the simple pendulum was approximated to that of simple harmonic motion, and the solution to the equation and the period of oscillation were also determined using the Mathematica 12.3 software technique. The solution and period of oscillation for the simple pendulum were compared with those of the simple harmonic oscillator, and the results showed differences in the values obtained for both cases. Even at the allowable approximation of the simple pendulum to the simple harmonic oscillator, which is   radian, differences in the values for both the simple pendulum and the simple harmonic oscillator still existed, although an accuracy correct to one decimal place was observed. This level of accuracy is not scientifically sufficient. This necessitated the assertion that the simple pendulum cannot be precisely approximated to simple harmonic motion for rigorous scientific investigation.