Simulation and Analysis of Pendulum Motion System with and Without Drag in the Absence of External Forces

The objective of this work is to conduct numerical simulations and analyses to derive the equations of motion of a non-torque pendulum. For the sake of obtaining pendulum motion equations under various circumstances, such as with and without a drag force, Taylor expansion, second-order differentiation, defined differential equation and other mathematic methods are employed. Moreover, Python is utilised for the calculation of precise values and the generation of graphs, thereby facilitating a more comprehensive understanding of the object's motion law and the interrelationship between its constituent elements. The article will predict the position of the ball in different conditions when there is a change of length, initial velocity or derivative angle. In this paper we first show the basic theory deduction and divided into two cases which are without drag and with drag. When there is no drag force, two conditions are discussed. One is Simple Harmonic Motion, and the other one is Regular Pendulum Motion. For both two cases, numerical and analytical solutions will be deduced. Furthermore, the paper is required to use control variable method to change certain elements and investigate the changes. Besides, when there is drag force, the conditions will be more complicated. For methodology part, there are defined differentiate equations, Largent Equation, Taylor Expansion and second-order derivation.