System of Pendulums Abstract

The purpose of this research is to further understand the pendulum system. Since pendulums are unsolvable differential equations, we are challenged to understand it using different approaches, such as simple harmonic motion, phase portraits, and Python simulations. These different approaches all bring something to the table to better understand the system. Also, since we used python, our workload was greatly reduced from time spent in computation. When looking at the probability aspect of the pendulum systems, different distributions are explored in order to further understand its motion. In addition, noise can be introduced in these systems in order to get a better understanding of the chaos and randomness which are seen in pendulums. Due to the consequence of noise, double pendulums should be unpredictable since probability cannot be applied in that specific situation.