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Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
Free and forced Vibrations
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Free and forced Vibrations

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  • 1. free and forced vibrations
  • 2. Free oscillators
    • Undamped oscillator
    • Natural frequency,  o
    • No external forces
    • e.g. swing
  • 3. Forced oscillators
    • External forces act on oscillator
    • Forced/driven oscillator
    • Resonance: driving  =  o
    • e.g. loudspeaker
    • vibrates in response to oscillating electric signal (driver)
    • Barton's pendulums
  • 4. Problems
    • Resonance driver applies forces that continually supply energy to oscillator  increasing amplitude
    • A increases indefinitely unless energy transferred away
    • Severe case: A limit reached when oscillator destroys itself
    • e.g. wine glass shatters when opera singer reaches particular note
  • 5. Damping
    • Resonant Amplitude limited by damping forces
    • At resonance:
    • rate of energy supply = WD against damping forces
    • Increasing damping reduces sharpness + strength of resonance
  • 6. Types of damping
    • Oscillating masses lose energy  amplitude decreases
    • Light damping: amplitude decreases gradually
    • Critical damping: amplitude decreases can decrease to zero without oscillation. Minimum time = T/4
  • 7. Q-factors
    • Measure of resonance
    • Definition: number free oscillations a free oscillator competes before decaying to zero *
    • Light damping = large Q factor
    • Heavy damping = small Q factor
      • e.g. Car = 1
      • Guitar string = 10 3
      • Watch quartz crystal = 10 5
    • * This is only an approximation. Q-factor does have a complicated precise mathematical definition
  • 8. Resonance and damping
  • 9. Examples
    • Pushing a child on a swing – maximum A when pushing  =  o
    • Tuning a radio – electrical resonance occurs when  o of tuning circuit adjusted to match  of incoming signal
    • Pipe instruments - column of air forced to vibrate. If reed  =  o of column loud sound produced
    • Rotating machinery – e.g. washing machine. An out of balance drum will result in violent vibrations at certain speeds
  • 10.
    • Investigation strength of chemical bonds – EM radiation = oscillating electrical disturbance. When incident on a crystal ions subjected to oscillating electrical force. At correct frequency ions ions oscillated by resonance
    • Energy is absorbed from radiation, the frequency of which can be measured with a spectrometer
  • 11. Unwanted resonance
    • Structures/machinery
    • Results in destruction
    • Damping
    • Changing  o of object by changing its mass
    • Change stiffness of supports (  moving resonant  away from driving  )
  • 12. Model aircraft being tested for resonance in a wind tunnel

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