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Amplitude vs frequency curve
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Resonance peak sharpens with lower damping.
The response curve peaks near ω₀ with width ≈ ω₀/Q. Less damping gives a taller and narrower peak.
Radio tuning with high Q has better selectivity.
Peak shifts slightly below ω₀ for heavy damping.
In more detail
The amplitude versus driving frequency curve shows a peak at resonance. The width and height of the peak depend on damping, with lighter damping giving a sharper, taller peak.
Real-world uses
- Engineers measure these curves to identify natural frequencies of structures.
- Audio equipment is characterised by its frequency response curve.
- Engineers plot amplitude against driving frequency to see how sharp the resonance peak is for a given damping.
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Frequently asked questions
What does the peak width tell me?
It is related to damping, so a narrow peak means low damping.
Does the peak occur exactly at the natural frequency?
For light damping, the peak is close to the natural frequency, but slightly shifted for stronger damping.
What happens to the peak when damping is reduced?
The peak becomes taller and narrower, which means the system is more sensitive to driving at its natural frequency.
Related topics in Oscillations & SHM
Forced oscillations · Resonance · Resonance examples · LC oscillations · Analogy between mechanical and electrical oscillators · Coupled oscillators