Resona

Meet Resona, an oscillator who rings loudest when pushed at her own natural frequency.

Any system with a restoring force and inertia, such as a mass on a spring, has a natural frequency at which it oscillates on its own: f₀ = (1/2π)√(k/m). A stiffer spring raises it; a heavier mass lowers it. Drive the system with a periodic push at that frequency and each push adds energy in step with the motion, so the response grows large. That is resonance.

A tuning fork is designed to ring at one pitch, such as the concert A of 440 hertz. Quadrupling the mass of an oscillator halves its natural frequency.

Resonance is useful: it is how musical instruments amplify sound, how a radio picks out one station, and how quartz crystals keep watches on time. It can also be dangerous: engineers design buildings and bridges so that wind and footsteps do not drive them at their natural frequencies.

Damping limits how large the resonant response can grow and broadens the range of frequencies that resonate. Real structures have many natural frequencies, not one.