The free pendulumThe movement of the bob can be plotted in a phase diagram. On the
horizontal axis the (angular) displacement is measured and on the vertical axis
the velocity is measured. The point of release is plotted at the point A on the
positive horizontal axis. At A the displacement is at a maximum and the velocity
is zero. As the bob moves through the vertical axis (where the displacement is
zero) the velocity is at a maximum, and this is plotted on the phase diagram at B.
At C when the bob is at the other extremity of its swing, the displacement is
negative and the velocity is zero. The bob then swings back through D (where it
is moving in the opposite direction so its velocity is negative) and completes one
swing at E. In the phase diagram this is represented by a rotation through 360
degrees, but because the swing is reduced the point E is shown inside A. As the
pendulum swings less and less this phase portrait spirals into the origin until
eventually the pendulum comes to rest.