Consider an elastic metallic beam suspended from a rigid frame over two magnets, equidistant from the undeformed position of the beam. The frame and magnets are fixed to a table that can be submitted to controlled periodic horizontal shaking. Depending on the amplitude and frequency of the shaking, there result three types of steady-state motion: (a) the beam oscillates periodically about one of the magnets, (b) oscillates periodically between the two magnets, or (c) meanders erratically in a chaotic sort of motion, punctuated by irregular visits to each of the equilibria. With this simple, engaging example Emil Simiu introduces us to the topic of his latest book, Chaotic Transitions in Deterministic and Stochastic Dynamical Systems.