To demonstrate a coupling resonance and to show normal modes.
Bar coupled pendula, as pictured.
By starting either pendulum in motion in the plane of the picture, one observes transfer of the motion between the two pendula. One can also produce the two normal modes: both pendula moving in phase, or the pendula moving out of phase.
J. Morris Blair, Laboratory Experiments Involving the Two-Mode Analysis of Coupled Oscillators, AJP 39, 555-557 (1971).