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P2214 Prelim 2 Formula Sheet f10

P2214 Prelim 2 Formula Sheet f10 - Physics 2214 Formula...

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Page 1 of 2 Physics 2214 Formula Sheet for Prelim 2 Damped and driven oscillations F = – k ( x – x eq ) 0 k m ϖ = F Damping = – b dx dt 0 0 eq / ( ) cos( ) τ ϖ φ - = + + A t x t A e t x τ Α = 2 m / b Q = 0 1 2 τ ϖ A F Drive = F 0 e i ω t 0 2 2 0 0 2 2 2 2 0 1 2 2 0 / ( ) (2 / ) / ( ) (2 / ) 2 / tan ( 0) ϖ ϖ ϖ τ ϖ ϖ ϖ τ ϖ τ φ π φ ϖ ϖ - = - + = - + = - - < < - D D A D D A D A D F m i F m A A ( 29 0 2 0 1 1 ϖ ϖ τ ϖ = - r A Mechanical Waves = y y t x v 2 2 2 2 y y t x = 2 v ± = u x t v τ μ = v 0 0 = - = - V p p p B V = - s p B x ρ = B v ph k ϖ = v gr d dk ϖ = v o o s s = + f f v+v v v ( 29 ( 29 2 2 2 a b a b cos a cos b cos cos + - + = ( ( ( ( ( cos a b cos a cos b sin a sin b + = - R = 1 2 1 2 - Z Z Z Z T = 1 1 2 2Z Z Z Z = μ v Z = ρ v R = 2 1 2 1 - v v v v T = 2 2 1 2v v v 2 1 3 Z Z Z =
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Page 2 of 2 ( 29 2 1 k 2 / u y t μ = ( 29 2 1 p 2 / u y x τ = y y P x t τ = - ( 29 2 1 k 2 / u s t ρ = ( 29 2 1 p 2 / u B s x = inst 0 s s s I p B t x t = - 2 2 v 1 v 2 2 m av m av p I Bk s u B
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