How does resonance occur?
Resonance is an enhanced response when a system is driven near frequencies associated with its natural oscillations. Swings, musical instruments, and electrical circuits provide different examples. Response amplitude depends on energy losses as well as driving frequency.
Natural frequency and damping
Mass, stiffness, and geometry determine natural frequencies. A periodic driving force can add energy at the appropriate phase and increase oscillation amplitude. Friction and other losses limit growth in real systems; unlimited growth in ideal linear models cannot be applied directly to reality. Greater damping usually produces a lower, broader response peak. Systems can also possess several vibration modes.
Why resonance matters in engineering
Bridge and machine designs aim to avoid operating conditions that strongly excite dangerous modes. Musical instruments deliberately use resonance to strengthen desired sounds. Not every structural vibration is resonance: driving frequency, mode shape, and damping must be examined together. Some wind-induced instabilities involve more complex interactions between airflow and structure than a simple resonance model can describe.