PhysicsChapter 3: Simple Harmonic Motion
Free, Forced Oscillations and Resonance
**Free oscillations** occur after an initial disturbance without a continuing external periodic force, while forced oscillations
Definition
Free oscillations occur after an initial disturbance without a continuing external periodic force, while forced oscillations are maintained by an external periodic driving force.
Free Oscillations
The system oscillates at its own: **natural frequency `f₀`** after being displaced and released.
Forced Oscillations
A periodic external force continuously drives the system. Example driving force: **F = F₀ cos(ωdt)** After transient effects fade, the steady response follows the driving frequency.
Resonance
When driving frequency approaches the natural frequency: **fd ≈ f₀** the response amplitude can become large. Damping limits the resonance amplitude in real systems.
Formula / Key Relation
Free natural angular frequency: **ω₀=√(km) Resonance condition approximately: ωd≈ω₀**
Exam preparation
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Review the key facts, formulas and checks before you move on.Free, Forced Oscillations and Resonance
Sticky Notes · Quick Revision
Free → `f₀`
- Forced → `f_d`
- Resonance → `fd ≈ f₀`
60-second revision
- Resonance is a special case of forced oscillation.
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