Damped & Forced Oscillations
Explore how damping and driving forces lead to resonance.
The Concepts
• Damping: A force (like friction) that removes energy from an oscillating system, causing its amplitude to decay over time.
• Forced Oscillation: An oscillation maintained by an external periodic driving force.
• Resonance: A dramatic increase in amplitude that occurs when the driving frequency matches the system's natural frequency ($ \omega_d \approx \omega_0 $).
What to look for
- More damping makes the swings die away faster.
- Resonance: when the driving frequency is close to the natural frequency ฯโ, the amplitude peaks. Watch the resonance curve.
Resonance Curve
Amplitude vs. Driving Frequency