Anyone who has pushed a child on a playground swing knows, without ever having studied physics, that timing matters more than strength — a small push delivered at exactly the right point in the swing's motion sends it soaring, while the same-sized push delivered at the wrong moment barely does anything, or even fights against the swing's existing motion. This is resonance: every oscillating system has a natural frequency it "wants" to move at, and energy transferred into that system in rhythm with its natural frequency accumulates far more effectively than energy delivered at a mismatched rhythm.
Every oscillating system has a frequency it prefers
A swing, left to move freely after being displaced, oscillates back and forth at a specific natural frequency determined by its own physical properties — for a simple pendulum-like swing, primarily its length. Pushing it in time with that natural frequency means each push arrives exactly when the swing is already moving in the same direction the push is applied, adding its energy constructively to the swing's existing motion, so the amplitude of the swing builds up over successive pushes. Pushing at some other, mismatched rhythm means pushes sometimes arrive while the swing is already moving the opposite direction, working against the existing motion and cancelling out some of the energy already built up, rather than adding cleanly to it.
The same principle drives standing waves in very different systems
The same underlying resonance principle governs a huge range of other oscillating physical systems that look, on the surface, nothing like a playground swing. A guitar string plucked or bowed vibrates most strongly at its own natural resonant frequencies, called its fundamental frequency and overtones, which is why a given string reliably produces the same pitch rather than an arbitrary one. Musical instruments, radio receivers tuned to a specific broadcast frequency, and many other engineered systems are deliberately designed around resonance, exploiting the same core principle that a system driven at its own natural frequency accumulates far more response than one driven at a mismatched rhythm — a pattern that shows up whenever a system has some natural frequency of oscillation and something is delivering energy to it in a repeating, rhythmic way.
What we're still unsure about
The core physics of resonance — that a system driven at its own natural frequency accumulates energy far more efficiently than one driven off that frequency — is well established classical mechanics, demonstrated reliably across an enormous range of physical systems. Where genuine engineering judgement, rather than a single formula, is still required is predicting exactly how a specific complex real-world structure will respond to a specific driving force, since a real bridge, building, or machine typically has multiple possible resonant frequencies and modes of vibration rather than one simple one, and working out which frequencies actually matter for a given structure's safety under realistic loading conditions requires detailed engineering analysis specific to that structure, not a single universal rule that applies identically everywhere.
This sits inside Standing Waves & Resonance, one of eight topics in Waves & Optics, one of five domains in Physics, one of seventeen subjects the app can quiz you on.