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Damped Oscillations

Damped Oscillations. Equation of motion. Forced oscillator with damping resistance force is proportional to speed : . For convenience: . Also, k=m w 0 2. In ‘complex’ method. Solution of damped harmonic motion. Define. Maximum amplitude at . or. -q. SB. Damped oscillation movie .

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Damped Oscillations

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  1. Damped Oscillations

  2. Equation of motion Forced oscillator with damping resistance force is proportional to speed :

  3. For convenience: Also,k=mw02 In ‘complex’ method

  4. Solution of damped harmonic motion Define

  5. Maximum amplitude at

  6. or

  7. -q SB

  8. Damped oscillation movie © Walter Fendt (2006) http://www.walter-fendt.de/ph14e/springpendulum.htm

  9. Average energy of the oscillator

  10. Plot of r2 vs w (near resonance)

  11. Work done by the force per second  Power

  12. Stored Energy

  13. Mean power

  14. Mean stored energy

  15. Efficiency of the oscillator Stored energy in oscillator Work done by force per cycle

  16. Another measure of response Q factor

  17. Summary Damped forced oscillation • Effect of damping is negligible at low and high frequency regime • Effect of damping is large near resonance • Increase in width and shift in resonance frequency with • an increase in damping

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