Analytical Mech Homework Solutions 179

Analytical Mech Homework Solutions 179 - 16 11.20 X...

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16 11.20 Generalized coordinates: X , sa () θ = y x ( x,y ) X M m a and sin (1 cos ) xXa ya = += cos sin θθ =+ = ±± ± 22 11 TM X m x y =++ ± 2 ( 2 cos sin MX m X a a ) =+ + + ( ) 1c o s Vm g ym g a == For small oscillations, in terms of the generalized coordinates X and s 2 1 2 X s V m g a ≈++ ± s 2 1 2 LTV M X mXs m g s a = ± Lagrange’s equations of motion yield … 00 g Xs s MmXm s a ++ = + + = Assuming … it X Ae s Be ω we obtain the matrix equation … 0 A ga B Mm m ωω  =  +  Setting the determinant of the above matrix equal to zero yields… 2 1 0 = , 2 2 gm M M + = The mode corresponding to 1 is … 0 0 A B =
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.

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