Why a small push at the right beat builds a huge swing: resonance and the narrow peak

Every child learns to pump a swing without a lesson: small shoves, well timed, build a huge ride, while big shoves at the wrong moment achieve nothing. That instinct is resonance.

Push a swing yourself, then let an auto-pusher drive it at any rhythm you choose and watch one narrow peak appear where the push matches the swing's own beat. Along the way: why a swing's period ignores the rider's weight, what the quality factor Q really measures, and why the wine-glass story is true but the Tacoma Narrows one is usually told wrong.