final_equation_sheet

final_equation_sheet - ME 274 Spring 2005 aP = i + + k x yj...

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ME 274 – Spring 2005 v P = x ˆ i + y ˆ j + z ˆ k v P = v P ˆ e t v P = r ˆ e r + r θ ˆ e a P =  x ˆ i + y ˆ j + z ˆ k a P = v P ˆ e t + v P 2 ρ ˆ e n a P = r r 2 ( ) ˆ e r + r + 2 r ( ) ˆ e dv dt = v dv ds v A = ω r A / IC d k dt = Ω× k v B = v A + × r B / A v B = v A + × r B / A + v rel B / A a B = a A + α × r B / A + × × r B / A ( ) a B = a A + × r B / A + × × r B / A ( ) + 2 × v rel B / A + a rel B / A U = F d r U 1 2 = T 2 T 1 = Δ T T = 1 2 mv 2 V e = 1 2 kx 2 V g = mgh G 2 G 1 = F ( ) t 1 t 2 dt H O = r × m v H O 2 H O 1 = M O ( ) t 1 t 2 dt I A = I G + md 2 I A = mk A 2 e = v 2 n f v 1 n f v 1 n i v 2 n i
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T = 1 2 mv G 2 T = 1 2 I O ω 2 T = 1 2 mv G 2 + 1 2 I G 2 m  x + c x + kx = 0 x + 2 ζω n x + n 2 x = 0 x = A 1 e ( ζ + 2 1 ) n t + A 2 e ( 2 1 ) n t x = A 3 + A 4 t ( ) e n t x = A 5 cos( d t ) + A 6 sin( d t ) ( ) e n t x = A 7 e n t sin( d t + ψ ) ( ) d = n 2 x + 2 n x + n 2 x = F 0 m sin( t ) x p = X 1 cos( t ) + X 2 sin( t ) x p = X sin( t φ ) X = F 0 / k 1 n 2 2 + 2 n 2 1 2 = tan 1 2 n 1 n
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final_equation_sheet - ME 274 Spring 2005 aP = i + + k x yj...

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