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EGM4313HW3

EGM4313HW3 - Page 551 problem 6 1 Bn 2k sin 1 sin 2 x 2 x 0...

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Page 551, problem 6: 1 0 1 1 0 0 1 2 sin sin 2 sin 2 2 sin sin sin 2 sin , 1 , 2 2 0, 3,4,5, , cos sin cos 2 sin 2 2 n B k x x n x dx k x n x dx k x n x dx k n k n n k u x t k t x t t Page 551, problem 7: x n t n n k t x u n k dx x n x x k B n n n n sin cos 1 12 ) , ( 1 12 sin 1 2 1 1 3 3 1 3 3 1 0 2 Page 546, problem 4: x n t n n k t x u n k dx x n x x k B n n n n sin cos 1 12 ) , ( 1 12 sin 1 2 1 1 3 3 1 3 3 1 0 2

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Page 556, problem 19: Let 2 2 ) ( ) ( ) ( ) ( ) ( ) ( ) , ( p x X x X t T c t T t T x X t x u as before. Solving for X : x L n t L c n C t x u C x u x L n t L c n C t L c n C t x u t L c n C t L c n C t T T L n c t T n L n p n n pL pL pL p t T A t L u px p t T A t x u px t T A t x u B t T B x u px A px B t T t x u px A px B x X t x x ) 1 2 ( sin ) 1 2 ( cos ) , ( 0 0 ) 0 , ( ) 1 2 ( sin ) 1 2 ( sin ) 1 2 ( cos ) , ( ) 1 2 ( sin ) 1 2 ( cos ) ( 0 ) 1 2 ( ) ( ,... 3 , 2 , 1 , 0 , ) 1 2 ( ,... 3 , 2 , 1 , 0 , ) 1 2 ( 0 ) cos( 0 ) cos( ) ( ) , ( ) cos( ) ( ) , ( ) sin( ) ( ) , ( 0 0 ) ( ) 0 , ( ) sin( ) cos( ) ( ) , ( ) sin( ) cos( ) ( 1 2 2 1 2 1 2 2 is a solution that satisfies the wave equation, both boundary conditions and the zero velocity condition. Linear superposition of such solutions also satisfy these conditions, hence
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EGM4313HW3 - Page 551 problem 6 1 Bn 2k sin 1 sin 2 x 2 x 0...

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