Quadratic damping

Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many models and is applicable to problems concerning aerodynamic and hydrological drag. In this article, we discuss how to use a generalized energy approach that permits us to discuss trajectories for initial value problems of dissipative oscillators like the harmonic oscillator and the pendulum having quadratic damping. This technique permits the computing of maximum deflections of a solution without having to compute the solution either analytically or numerically. This discussion is suitable for classroom presentation and for computer laboratory investigation.