Analytical Mech Homework Solutions 177

Analytical Mech Homework Solutions 177 - 14 The homogeneous...

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14 The homogeneous equations (Equations 11.4.10) for the two components of the j th eigenvector are … 22 1 12 2 0 j j a lg l a ll g ωω  −+ =  −− +  Inserting the larger eigenfrequency (the (+) solution for 2 ω above) into the upper homogeneous equation yields the solution for the components of the 1 st eigenvector … () 1 1 11 2 1 21 a l a −+ − = 0 2 1 2 12 1 11 21 21 l l ga ga  ++ + +  −=  2 1 2 21 11 2 ll l l aa l + = for the higher frequency, anti-symmetric mode. Inserting the smaller eigenfrequency (the (-) solution for 2 ) into the upper homogeneous equation yields the solution for the components of the 2 nd eigenvector … 1 2 12 2 2 22 a l a = 0 22 12 2 l + = for the lower frequency, symmetric mode. Again, we let a 11 = 1 and a 21 = 1, since only ratios of the components of a given eigen vector can be determined.
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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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