This section covers my work with Pendulums. I have applied the Parker-Sochacki method to update the equations of motion for a simple pendulum, driven pendulum, and damped-driven pendulum. I also have a section that shows that Parker-Sochacki, when its accuracy is increased, conserves energy. I also have a section that compares different numerical methods in the industry in terms of conservation of energy and Parker-Sochacki is shown to be the best option. I compare Forward Euler, Semi-Implicit Euler, Verlet, Runge-Kutta 2 Midpoint Method, and Runge-Kutta 4th Order.