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Free, Forced Oscillations and Resonance
Free oscillations occur after an initial disturbance without a continuing external periodic force, while forced oscillations are maintained by an external periodic driving force.
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Free, Forced Oscillations and Resonance
Push a swing once and leave it: free oscillation.
Keep pushing it repeatedly: forced oscillation.
Push at just the right rhythm: resonance.
Recommended for Class 12
Free, Forced Oscillations and Resonance
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**
Free, Forced Oscillations and Resonance — Advanced
The driven damped oscillator obeys:
**mẍ+bẋ+kx=F₀cos(ωdt)**
Its steady-state amplitude depends strongly on driving frequency and damping.
Common Mistakes
Common Mistakes
- Mistake
Do not define every forced oscillation as resonance.
- Mistake
Resonance occurs only under the appropriate frequency condition.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Resonance is a special case of forced oscillation.
A system undergoing free oscillation vibrates at its natural frequency after an initial disturbance. Forced oscillations are maintained by a periodic external force. When the driving frequency approaches the system's natural frequency, resonance occurs and the oscillation amplitude can become large. Real damping limits this amplitude.
- Definition
- A system undergoing free oscillation vibrates at its natural frequency after an initial disturbance. Forced oscillations are maintained by a periodic external force. When the driving frequency approaches the system's natural frequency, resonance occurs and the oscillation amplitude can become large. Real damping limits this amplitude.
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Practice
PQ
Q1. Define free oscillation
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Q2. Define forced oscillation
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Q3. Define resonance
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Q4. What limits resonance amplitude?
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Q5. Give one example
Exam Practice
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Q1. Differentiate free and forced oscillations
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Q2. Explain natural frequency
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Q3. Explain resonance
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Q4. Explain the role of damping at resonance
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Q5. Give applications or consequences of resonance
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.