Publisher Summary This chapter provides an overview of applications of higher order differential equations. It reviews the procedures that lead to the differential equations that model simple harmonic motion and damped motion. Another situation that leads to a second order ordinary differential equation is that of the simple pendulum. In this case, a mass (m) is attached to the end of rod of length (L) that is suspended from a rigid support. As the motion is best determined in terms of the angular displacement t, θ = 0 is let to correspond to the rod hanging vertically. The objective is to find the motion of the mass as a function of θ, an initial position and an initial velocity. Assuming that the pendulum is allowed to rotate without friction, the only force acting on the pendulum is that of the gravity. Newton's second law and the relationship s = Lθ are used to establish the initial value problem.