ASE 365 - Lecture 33 - Solutions for Test 2 1 Problem ) sin...

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Unformatted text preview: Solutions for Test 2 1 Problem ) sin cos ( 2 ) ( sin (sin 4 2 cos )) 2 ( sin( 4 2 cos ) ( sin sin ) ( t t t k F t t t t m F t t m F d t m F t x n n n n n n n n t n n n n t n n n +- = -- 1 +- = - 1 +- =- = : integral n convolutio by Response a) ) ( sin t u t F kx x m n = + : to according excited ICs, zero with system SDOF Undamped Solutions for Test 2 1 Problem ) ( 2 ) ( ) ( ) sin cos ( 2 ) ( = +- = = +- = n n n n n k F x x t t t k F t x , : ICs Satisfying b) ) ( sin t u t F kx x m n = + : to according excited ICs, zero with system SDOF Undamped Solutions for Test 2 2 Problem 2 2 2 2 2 2 2 2 2 2 2 2 2 2 ) ( 2 2 1 ) ( 2 1 ) ( + = + + + +- = + s s s s s : that verify First, : transforms Laplace using solve problem Same- ( 29 t t t k F t t t m F t x s s s s m F s m F s X s m s G s F s F t F t F n n n n n n n n n n n n n n n n n n sin cos 2 sin 1 cos 2 ) ( ) ( ) ( 2 1 ) ( ) ( 1 1 ) ( ) ( sin ) ( 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 +- = +- = + + + +-- = + = + = + = = so , so , and , , For Solutions for Test 2 3 Problem = + 4 3 / 2 / 2 / 2 2 2 x kL kL kL k x mL mL mL m : by governed system 2DOF [ ] ) 12 / 5 3 / 7 3 ( ) 2 / 1 ( ) 3 / 1 )( 2 4 ( ) / ( ) 3 / 1 ( ) 2 / 1 ( ) 2 / 1 ( 2 4 ) det( 2 2 2 2 2 2 2 2 2 2 = +- =---- = =---- =- L k L k k m L L L k M K : modes and s frequencie Natural a) k m k m 5 18 2 5 18 2 5 36 25 196 5 14 5 36 5 28 2 2 2 1 2 = = =- = = +- , , Solutions for Test 2 3 Problem = = = --- - =- 1 ) 3 / 2 1 ( ) 2 / 2 1 ( ) 2 / 2 1 ( 2 2 4 ) ( 21 11 21 11 21 11 2 1 2 1 1 u u u u u u L L L k M K u u : For a) - = = ---- = ---- =- L u u u u L L L k u u L L L k M K / 4 1 4 4 16 5 ) 5 / 6 1 ( ) 5 / 9 1 ( ) 5 / 9 1 ( 5 / 36 4 ) ( 22 12 22 12 2 22 12 2 2 2 2 2 u u : For Solutions for Test 2 3 Problem : n translatio pure , : mode First a) = = 1 x e T e e L L e e L L L x x L L e e = - = - =...
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This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

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ASE 365 - Lecture 33 - Solutions for Test 2 1 Problem ) sin...

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