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phy293_l04.page1 - PHY293 Oscillations Lecture#4 1 First...

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PHY293 Oscillations Lecture #4 September 18, 2009 1. First problem set ( http://www.physics.utoronto.ca/ phy293h1f/waves/phy293 ps1.pdf ) Due Monday at 5:00pm 2. Flash Demo ( http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/ClassMechanics/DampedSHM/DampedSHM.swf ) Start of material 1. Quality of an Oscillator The equation of motion: ¨ x + γ ˙ x + ω 2 0 x = 0 has two quantities with dimensions of 1/time: ω 0 and γ Their ratio is dimensionless: Q = ω 0 γ known as the Quality of the oscillator When Q is large the dissipation is small and the oscillations continue for a long time. Number of oscillations a system undergoes ’til energy falls to e - 1 of its original value (about 37%) is: 2 πn osc = ω 0 t e Where t e is the e-folding time thus: n osc = ω 0 γ 1 2 π = Q 2 π Note: last substitutions only holds for large Q (when ω 0 ω 0 ) In terms of enegy Q is related to the ratio: energy stored in oscillator/energy lost per cycle E Δ E = E 2 π γ ω 0 E = Q 2 π 2. Overdamped Solution Consider the other cases: x = C
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