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Exercise:
The amplitude of an oscillator with with period TO exponentially decreases from AaO to AbO within tO. Calculate the damping coefficient and the damping ratio.

Solution:
The decrease in amplitude is given by fracA'A e^-delta t Solving for the damping coefficient yields delta deF -fracttimeslnfracAbAa de approx resultdeP The angular frequency is omega fracpiT It follows for the damping ratio zeta fracdeltaomega zeF fracdetimesTpi resultzeS Since zetall the oscillation is only lightly damped.
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Exercise:
The amplitude of an oscillator with with period TO exponentially decreases from AaO to AbO within tO. Calculate the damping coefficient and the damping ratio.

Solution:
The decrease in amplitude is given by fracA'A e^-delta t Solving for the damping coefficient yields delta deF -fracttimeslnfracAbAa de approx resultdeP The angular frequency is omega fracpiT It follows for the damping ratio zeta fracdeltaomega zeF fracdetimesTpi resultzeS Since zetall the oscillation is only lightly damped.
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Branches
Damped Oscillations
Tags
damping coefficient, damping ratio, exponential envelope, linear damping
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Difficulty
(2, default)
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0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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