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Natural frequency, f₀
● VERBATIM — examined word-for-wordThe frequency at which a system oscillates freely when displaced and released, with no external driving force and negligible resistive forces.
What this actually means
Displace the system, let go, and interfere no further: the frequency it chooses for itself is f₀. It is a property of the system, set by its stiffness and inertia, not of anything driving it.
'Freely', 'no external driving force' and negligible resistive forces are the definition's working parts; each one is checkable in a mark scheme.
f₀ is the frequency a driver must match to cause resonance, which is why the definition matters beyond itself.
Prove it — watch it be true
- Switch to free damping with light damping
- Displace and release: the system rings at one particular frequency
- That self-chosen frequency is f₀ — no driver anywhere in sight