Damped Oscillations.

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Presentation transcript:

Damped Oscillations

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

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

Solution of damped harmonic motion Define

Maximum amplitude at

or

-q SB

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

Average energy of the oscillator

Plot of r2 vs w (near resonance)

Work done by the force per second  Power

Stored Energy

Mean power

Mean stored energy

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

Another measure of response Q factor

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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