Resonance & Forced Oscillation
Amplitude vs driving frequency resonance curve. Maximum amplitude at ω_drive ≈ ω₀. Adjustable damping, spring constant, mass, and driving force.
WHAT IS RESONANCE?
Resonance occurs when an external periodic force is applied to a system at its natural frequency (). This results in a massive increase in the amplitude of oscillation because the external force is perfectly timed to add energy to the system during every cycle.
THE MECHANISM
Every physical system has a natural frequency. If you push a swing at its natural frequency, it goes higher and higher. If you push it too fast or too slow, your efforts cancel out. Resonance is found in musical instruments, bridges, and even atomic structures.
HOW TO USE THIS VISUALIZATION
1. **Set Driving Frequency**: Change the frequency of the external motor ().\n2. **Observe Amplitude**: Watch the system response as approaches .\n3. **Analyze the Phase**: Notice the phase shift between the driver and the oscillator at resonance.\n4. **Change Damping**: See how more friction results in a wider, lower resonance peak.
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 7: Oscillations (Topic 7.3)
Learning Objective: 7.3.1
COMMON MISCONCEPTIONS
- Thinking resonance can happen at any frequency (it must be close to a natural frequency).
- Believing amplitude grows to infinity in real systems (damping limits the maximum amplitude).
- Confusing forced oscillation with free oscillation.
KEY TAKEAWAYS
- Resonance occurs at the natural frequency.
- Amplitude increases dramatically.
- Damping affects the sharpness of the resonance peak.
- Phase shift is 90 degrees at resonance.
PRACTICE QUESTIONS
Q1 (CONCEPTUAL): What happens to the amplitude of a system when the driving frequency matches the natural frequency?
Show Answer & Explanation
Answer: It reaches a maximum.
Explanation: This is the condition of resonance where energy transfer to the system is most efficient.
