State the coupled pendula ODEs using matrices

In this video, we analyze the forces acting on each pendulum using free-body diagrams. We use this analysis of net forces to state a pair of coupled ordinary differential equations that describe the behavior of the masses and we rely on matrices to do so. This matrix equation is in the classic “stiffness” form. This matrix sets the foundation for our transformation of this problem into a standard eigenvalue problem. Moreover, this matrix structure shows up in many application areas and is the foundation for the famous finite element methods matrix structure. Congratulations y’all: we have officially graduated to a matrix problem and linear algebra is so close we can smell it… 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...