10_1425_web_Lec_29_DampedDrivenOscillator

10_1425_web_Lec_29_DampedDrivenOscillator - Damped and...

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Damped and Driven Harmonic Motion Physics 1425 Lecture 29 Michael Fowler, UVa

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Damped Harmonic Motion In the real world, oscillators experience damping forces: friction, air resistance, etc. These forces always oppose the motion: as an example, we consider a force F = bv proportional to velocity. Then F = ma becomes: ma = kx bv That is, C Extension x F kx = − F bv = − Spring’s force m Drag force 22 / /0 md x dt bdx dt kx + += The direction of drag force shown is on the assumption that the mass is moving to the left .
Underdamped Motion The equation of motion has solution where Plot: m = 1, k = 4, b = 0.11 22 / /0 md x dt bdx dt kx + += cos t x Ae t γ ω = ( ) ( ) /2 , / /4 bm km b m = =

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Underdamped Motion The point to note here is that the damping can cause rapid decay of the oscillations without a perceptible change in the period (around 0.04% for b = 0.11, k = 4, m = 1).
Underdamped Motion Compare the curve with the equation: the successive position maxima follow an exponential curve , so any maximum reached

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This note was uploaded on 12/07/2011 for the course PHYSICS 1425 taught by Professor Michaelfowler during the Spring '10 term at UVA.

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10_1425_web_Lec_29_DampedDrivenOscillator - Damped and...

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