Analytical Mech Homework Solutions 185

Analytical Mech Homework Solutions 185 - 22 Initial...

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22 Initial conditions are: 10 23 123 10 ; 0; 0 o θθ θ == === ±±± The conditions generate 6 equations with 6 unknowns and solving gives … 00 11 cos cos 22 tt 3 ωω =+ 21 cos cos 3 =− cos cos 3 11.23 See Ex. 11.4.1, page 497-498 The amplitudes of the eigenvectors are … 12 3 1 2 1 mM   == =  aa a K - Matrix M - Matrix m M m = M K- K0 =- K 2 K - K 0- KK K 11 1 0 1 1 1 10 1 2 1 02 1 0 1 diag KKK m M K K −− ² K AKA 0 0 8 8 diag K m MK = + K 0 0 1 0 0 1 100 1 diag m M m ² MA M A 2 200 0 2 4 diag m mmM + = + M So, we have … 2 1 0 ω = , 2 2 2 2 mm , and … ( ) () 2 3 2 14 4 28 8 24 1 2 Km M m M m m m M ++
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