  The 1:1:2 resonant elastic pendulum is a simple classical system that
displays the phenomenon known as Hamiltonian monodromy. With suitable initial
conditions, the system oscillates between nearly pure springing and nearly pure
elliptical-swinging motions, with sequential major axes displaying a stepwise
precession. The physical consequence of monodromy is that this stepwise
precession is given by a smooth but multivalued function of the constants of
motion. We experimentally explore this multivalued behavior. To our knowledge,
this is the first experimental demonstration of classical monodromy.
