3221test2Formulae - F = mv 2 /r F = mω 2 r ω = 2 π/T L =...

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1 Name: Phy 3221 Test # 2 April 6, 2011 Formula Sheet ~ F = m~a ~ F = - ~ U ( ~ r ) = - ∂U ( ~ r ) ∂~ r ax 2 + bx + c = 0 x = - b ± b 2 - 4 ac 2 a For circular coordinates in two dimensions: ˙ ˆ r = ˙ θ ˆ θ ˙ ˆ θ = - ˙ θ ˆ r ~ r = r ˆ r ~v = ˙ r ˆ r + r ˙ θ ˆ θ ~a = (¨ r - r ˙ θ 2 r + (2˙ r ˙ θ + r ¨ θ ) ˆ θ ~ U ( x,y,z ) = ∂U ∂x ˆ ı + ∂U ∂y ˆ + ∂U ∂z ˆ k m ¨ x + kx = 0 x ( t ) = A sin( ωt + φ ) x ( t ) = A cos( ωt + φ ) ω = 2 π T = r k m ¨ x + 2 β ˙ x + ω 2 0 x = 0 , 2 β = b/m x ( t ) = Ae - βt cos( ω 1 t - δ ) , ω 1 = q ω 2 0 - β 2 x ( t ) = ( A + Bt ) e - βt x ( t ) = e - βt ± A 1 e λt + A 2 e - λt ² , λ = q β 2 - ω 2 0
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2 ¨ x + 2 β ˙ x + ω 2 0 x = B cos( ωt ) , B = F 0 /m x h ( t ) = A 1 e - βt sin( ω 1 t + φ ) , ω 1 = q ω 2 0 - β 2 x h ( t ) = A 2 e - βt cos( ω 1 t + φ ) x h ( t ) = e - βt ± A 1 e λt + A 2 e - λt ² , λ = q β 2 - ω 2 0 x p ( t ) = B p ( ω 2 0 - ω 2 ) 2 + 4 ω 2 β 2 cos( ωt - δ ) δ = tan - 1 ³ 2 ωβ ω 2 0 - ω 2 ´ Q = p ω 2 0 - 2 β 2 2 β U = - Gm 1 m 2 r F = Gm 1 m 2 r 2 ω 2 = g/‘
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Unformatted text preview: F = mv 2 /r F = mω 2 r ω = 2 π/T L = L p 1-v 2 /c 2 T = T o / p 1-v 2 /c 2 x = x-vt p 1-v 2 /c 2 x = x + vt p 1-v 2 /c 2 u x = u x + v 1 + u x v/c 2 t = t-vx/c 2 p 1-v 2 /c 2 t = t + vx /c 2 p 1-v 2 /c 2 u y = u y p 1-v 2 /c 2 1 + u x v/c 2-c 2 Δ τ 2 =-c 2 Δ t 2 + Δ x 2 + Δ y 2 + Δ z 2 3...
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This note was uploaded on 12/15/2011 for the course PHY 3221 taught by Professor Chan during the Spring '08 term at University of Florida.

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3221test2Formulae - F = mv 2 /r F = mω 2 r ω = 2 π/T L =...

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