Wilberforce PendulumA mass hangs from a spring that is free to both stretch and twist. Pull it straight down and let go: it bounces up and down for a while — then, with nothing new pushing it, the bounce dies away and the mass starts twisting instead. Wait a little longer and the twisting dies away too, handing all the motion straight back to bouncing. It trades one kind of motion for the other, forever.L.R. Wilberforce built one in 1896 by tuning a spring's stretch and twist frequencies to match. Because they're coupled, the two straight-line equations of motion aren't the true rhythms of the system; add and subtract them and two clean normal modes fall out, oscillating at slightly different frequencies ω⁺ and ω⁻. Stretch and twist are just that pair beating against each other — the same two-tone beat you hear from two nearly-matched piano strings, here swapping energy between up-down and round-round instead of loud and quiet.