Why some vibrations grow out of control — and why the fix is almost never just "make it stiffer."
Every mechanical system — a beam, a shaft, a floor, a bridge deck, a bracket — has a frequency it "wants" to vibrate at if you disturb it and let it swing freely. Nudge most structures and they'll oscillate at that one frequency and quietly decay. But apply a repeating force atthat same frequency, and the response stops being quiet. Each push arrives in sync with the structure's own motion, adding energy on top of energy already stored, and the amplitude can grow to many times what the same force would produce at any other frequency. That phenomenon is resonance, and it is one of the most consequential ideas in mechanical and structural design.