Simple mechanical analogs of rapid adiabatic passage in atomic physics

We discuss two mechanical systems in which the approximate equations of motion are the same as the rapid adiabatic passage of a two-state quantum-mechanical system, such as that which occurs with quasistatic interactions and from the quasiperiodic action of a chirped-frequency laser pulse. We discuss a pair of masses on springs, weakly coupled by another spring, one of whose spring constants varies slowly, and a pair of coupled pendula, where the length of one pendulum slowly changes. In each example an approximation analogous to the rotating-wave approximation used in the corresponding quantum system brings the second-order macroscopic equations of motion into first-order form, and a slow variation in a system parameter characteristic leads to adiabatic change and rapid adiabatic passage.