#### Exercise 1: Euler-Cromer Model of the Rigid Pendulum

Build a computational model of a plane undamped, unforced rigid pendulum using the Euler-Cromer method. Assume your pendulum consists of a rigid metallic rod, one meter in length, with a mass of 1kg. Also assume that one end of the rod is fixed to an immovable support, and that the rod is free to rotate without bound in a plane. For initial conditions, assume the rod is displaced at some angle, greater than 90∘, relative to its vertical minimum potential energy configuration, and released from rest. This physical situation has no exact analytical solution with which you will be able to compare the results of your computational model, so you must carefully determine a value of Δ t that produces an accurate approximation without the benefit of making a comparison. Describe in detail the procedure you used in arriving at an acceptably small value of Δ t, show plots of the angular displacement and angular velocity as functions of time, and comment on the pendulum’s dynamic behavior. Is the behavior of your computational model what you expect for a real pendulum?