Numerical Simulation of a Chaotic System

Author

Hind Khalifa

Mentor

Vasiliy Znamenskiy PhD

Abstract

This project demonstrates use of computational methods to analyze an atypical problem in oscillatory physics: harmonic motion. The purpose is to show the mathematical equation that describes the motion of a simple pendulum with a defined point mass suspended from a string with relatively negligible mass to the pendulum bob, implemented in Python and Google Colab. The model calculates the main parameters of angular frequency, frequency, and period given L (length of pendulum string) and g (acceleration due to gravity/weight of bob).
A central goal of the project is to utilize formulae in numerical simulation to produce final values quickly and effectively. This computational approach not only simplifies the problem but allows us to compare multiple problems with varying independent variables. This helps students understand theory, formulae, application, and analytical graphical representation better.
Google Colab will be used to integrate code, value tables, and graphs in a single document to show the results in such a way that interpretation will be significantly easier. Overall this project aims to demonstrate simple and atypical computational problems by means of efficient problem-solving, clarity of solutions plotted, and accessibility of data analysis.