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L4_31mar08 - Please pick up your clicker Ideal and damped...

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Ideal and damped oscillations In ideal oscillations, the total energy is conserved: In damped oscillations, energy is lost with time: b represents damping. ϖ ’ is almost the same as ϖ if b is small. 2 time 2 2 1 time 2 2 mgh kx 2 1 mv 2 1 mgh kx 2 1 mv 2 1 + + = + + ( 29 ( 29 2 2 m 2 bt m m 2 b m k ' t ' cos e X X - = ϖ φ + ϖ = -
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Damped oscillations: Underdamped (small b): Critical damping is when Overdamping is when = m k m 2 b m k m 2 b = m k m 2 b
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Driven oscillations Driven oscillations generally have a resonant frequency. The oscillation amplitude is largest if driven at the resonant frequency. NOT PROVEN: Small damping gives a sharply peaked amplitude versus frequency curve, while large damping gives a flatter curve.
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100% 0% 0% 0% 0% 0% 0% 0% 0% 1 1 of 5 Rank the sinusoidal waves shown below according to their wavelengths.
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