We have generated a number of phase‐space diagrams for several physically significant differential equations, including those describing the motion of a driven, damped pendulum and a Josephson weak link. These phase‐space diagrams can lead to considerable insight into the complex behavior exhibited by these systems. A number of these phase‐space diagrams were generated with parameters that can be duplicated with suitable mechanical models, allowing them to be used in conjunction with such models for a detailed study of the behavior of the driven, damped pendulum and Josephson weak link.