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Analytical Mech Homework Solutions 141

Analytical Mech Homework Solutions 141 - 1 m mg 2 x x(b T =...

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(b) 2 2 1 2 2 m x m x m x 2 T m = + = + ± ± ± and 2 2 2 x x m gx m g mgx x l l = − = − g V m 2 2 2 2 m m L T V m x mgx x l = = + + + ± g ( ) 2 L m m x x = + ± ± , ( ) 2 d L m m x dt x = + ±± ± L m mg x g x l = + ( ) 2 m g m m x mg x l + = + ±± 2 g ml m x x l m m + = + ±± 10.5 The four masses have positions: m 1 : 1 2 x x + m 2 : 1 1 l x x 2 + m 3 : 2 2 l x x 3 + m 4 : 2 2 3 l x l x 3 + ( ) ( ) 2 1 1 2 V g m l x x = − + 1 1 2 m x x + + ( ) ( ) 3 2 2 3 4 2 2 3 3 m l x x m l x l x + + + + ( ) ( 2 2 1 1 2 2 1 2 1 2 T m x x m x x = + + + ± ± ± ± ) ) ( ) ( 2 2 3 2 3 4 2 3 m x x m x x + + + ± ± ± ± ( ) ( ) ( ) 2 2 1 1 2 2 1 2 3 2 3 1 1 1 2 2 2 L T V m x x m x x m x x = = + + + + + ± ± ± ± ± ± 2 ( ) ( ) ( ) ( ) 2 4 2 3 1 1 2 2 1 2 3 4 3 3 4 1 . 2 m x x gx m m gx m m m m gx m m cons + + + + + + ± ± t ( ) ( 1 1 2 2 1 2 1 L m
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