Simulation of Simple Pendulums with Different Stages

One of the main topics in classical mechanics is the study of pendulum motion, which makes it possible for us to know how objects move and swing. In this study, two approachesnumerical and analyticalfor simulating pendulum motion under various beginning conditions are compared. It also looks at more intricate situations. Pendulum research was first developed in the late 16th century by Galileo Galilei and further advanced by Christiaan Huygens, the man who invented the pendulum clock. With the passage of time, scientists were able to describe pendulum motion with much greater accuracy because of developments in mathematics, such as the differential calculus created by Leibniz and Newton. The development of digital computers and numerical techniques made it possible to solve difficult issues, such as pendulum motion. This research investigates the motion of the fundamental pendulum by assuming only modest oscillations and eliminating air resistance. Analytical procedures construct mathematical equations using Newton's principles when numerical processes divide motion into tiny steps for approximative solutions. The research investigates and assesses the advantages and disadvantages of various approaches. The results show that for real-world scenarios such as air resistance, numerical methods perform better than purely analytical methods. This comparison highlights the need to use both approaches to fully understand mechanical systems and may be useful for future motion research.