Resonance is the large-amplitude response of an oscillating system when its driving frequency is equal or close to its natural frequency. Natural frequency is the frequency at which the system oscillates freely after being displaced and released.
Every oscillating system has one or more natural frequencies determined by its physical properties. For example, an ideal mass and spring system has
where is the spring constant and is the oscillating mass. A stiffer spring increases , while a larger mass decreases it.
In a driven oscillation, an external periodic force supplies energy to the system. When the driving frequency approaches , the force transfers energy efficiently because it acts with a favorable phase relationship to the motion. The oscillation amplitude therefore becomes large, producing resonance.
| Concept | Meaning |
|---|---|
| Natural frequency | Frequency of free oscillation after an initial displacement |
| Driving frequency | Frequency of the external periodic force |
| Resonance | Maximum response when the driving frequency is equal or close to the natural frequency |
| Damping | Energy dissipation that reduces the resonant amplitude and broadens the resonance peak |
With light damping, the resonance peak is high and narrow. Greater damping produces a lower, broader peak; it can also make the resonant frequency slightly lower than the undamped natural frequency.
A common misconception is that resonance creates energy or always causes an infinite amplitude. It does neither: energy comes from the driving force, and real systems lose energy through damping, which limits the amplitude.
This is SL and HL content in C.4 Standing waves and resonance, with no separate AHL extension. For an Explain question, link the matching frequencies to efficient energy transfer and increased amplitude. Do not merely state that “the frequencies are equal”; identify the driving and natural frequencies and describe the role of damping.
