resonance
Resonance is the dramatic build-up that happens when you push something at exactly its favourite rhythm. Push a swing in perfect time and it climbs higher and higher; sing the right pitch and a wine glass can shatter; rock a stuck car back and forth at the right moment and it lurches free. The everyday secret is timing: adding a little energy in step, cycle after cycle.
Precisely, resonance occurs when the driving frequency of an external periodic force matches, or comes close to, the system's own natural frequency omega_0. At that match the steady-state amplitude of the driven oscillation reaches a peak. How tall and sharp that peak is depends on damping: with very little damping the peak is enormous and narrow, while more damping makes it lower and broader.
Resonance is everywhere useful, from tuning a radio to a station's frequency (electrical resonance in an LC circuit) to the rich tone of musical instruments and the physics behind MRI. It can also be destructive, as in vibrating machinery or bridges. Two honest points: resonance needs both a driving force and a matching natural frequency, so a lone oscillator does not resonate by itself; and the effect is not that the force becomes huge, but that energy is fed in exactly in step every cycle, so it accumulates.
Tuning a radio works by resonance: you adjust the circuit's natural frequency until it matches the frequency of one station's broadcast, so that signal is amplified strongly while all the others stay weak.
Match the driving frequency to the natural frequency and the response peaks; less damping makes the peak sharper.
Resonance needs both a driving force and a matching natural frequency; it works not because the force is large but because energy is added in step every cycle.