coupled oscillation - 1. Equation of motion : ) ( 2 1 1 1 x...

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Unformatted text preview: 1. Equation of motion : ) ( 2 1 1 1 x x kx x m--- = , ) ( 1 2 2 2 x x kx x m--- = 2. Looking for normal mode in which all masses oscillate at the same frequency - t i e a t x 1 1 ) ( = , t i e a t x 2 2 ) ( = 3. After replacement, eqns. of motion reduce to = ---- 2 1 2 2 a a k m k m 4. For as to be nontrivial (non-zero), determinant of the 2*2 matrix should be zero. m k = 2 (low freq. with 2 1 a a = ; move-together(MT) mode), m k 2 2 + = (high freq. with 2 1 a a- = ; mirror symmetry(MS) mode) 5. Normal coordinates : 2 ) ( ) ( ) ( 2 1 1 t x t x t + = , 2 ) ( ) ( ) ( 2 1 2 t x t x t- = 6. For MT mode, 1 & 2 = , while 1 = & 2 for MS. These are brief summary of what weve covered during the section today. But lets try to keep moving a little bit further into the true meaning of normal mode....
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coupled oscillation - 1. Equation of motion : ) ( 2 1 1 1 x...

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