How to linearize the nonlinear ODE for a simple pendulum

In this video, we show how to linearize our second-order nonlinear ordinary differential equation (ODE) for the motion of a single pendulum. We discuss the process of transforming our nonlinear ODE into a linear ODE using our small angle approximation. We then show how this assumption effects our derivation and arrive at a new linear approximation in the form of a simple harmonic oscillator. Viewers can find much more about the McCusker apparatus and an authentic modeling activity that gives rise to a standard eigenvalue problem in the real world on the support website for this project: http://www.appliedlinearalgebra.com/b...