← all cardsTopic 8 · Oscillations · Forced oscillations & resonance
Why keep f₀ OUT of the operating range
Loudspeaker cone (N09): if the cone's natural frequency sat inside the audio range, signals near it would resonate — that frequency reproduced with exaggerated amplitude, distorting the sound. Same logic for machine mounts, buildings, bridges: design f₀ away from the driving frequencies the system will meet.
What this actually means
The loudspeaker classic: if the cone's natural frequency sat inside the audio range, any signal near it would resonate and be reproduced with exaggerated amplitude, distorting the sound.
Same design logic everywhere: machine mounts, buildings, bridges. Place f₀ well away from the driving frequencies the system will actually meet in service.
Prove it — watch it be true
- Sweep f_d across a working range containing f₀
- Every crossing of f₀ produces an exaggerated response spike
- Now imagine f₀ moved outside the sweep: flat, faithful response — the design goal