(455) Resonance and damping [IB Physics SL/HL]

Definition: The frequency at which a system can readily vibrate without friction or damping.
Examples:
- Greenhouse gases absorb infrared light due to their natural frequency, contributing to atmospheric warming.
- Mass on a spring oscillates at its natural frequency dependent on the system's characteristics.
Relationship Between Frequency and Period:
- Inversely proportional, with formulas:
  - Period: ( T = \frac{1}{f} )
  - For a spring-mass system: ( T = 2\pi \sqrt{\frac{m}{k}} )
  - Natural frequency: ( f_0 = \frac{1}{2\pi} \sqrt{\frac{k}{m}} )

Resonance: Occurs when the driving frequency matches the natural frequency, increasing amplitude.
Applications:
- Bridges must avoid natural frequencies close to common vibrations (e.g., people walking).
- In glass resonance, matching frequency can create standing waves and potentially break the glass.
- Microwave ovens exploit water's resonant frequency to heat food.

Definition of Damping: Friction that reduces amplitude over time.
Types of Damping:
- Underdamped: Allows oscillation but reduces amplitude gradually.
- Overdamped: System returns to rest without oscillation.
- Critically Damped: Returns to rest quickly without overshooting.

General Principle: As damping increases, amplitude decreases.
Influence of Damping on Resonant Frequency:
- Increased damping shifts the peak amplitude downwards and leftward in frequency.
- Observation: Light damping results in lesser amplitude and shifts resonance peak frequency to the left.
- Summary:
  - No damping: full resonance and maximum amplitude.
  - Light damping: amplitude decreases, and frequency shifts left.
  - Excess damping stops oscillations entirely.

Key Takeaways:
- Natural frequency determines how a system vibrates.
- Resonance can amplify vibrations if driven at the natural frequency.
- Damping counteracts vibration amplitude and shifts frequency response leftward.