Solutions for Test 2

# Solutions for Test 2 - 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 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ τ ϖ ϖ ϖ τ ϖ τ τ ϖ τ ϖ ϖ +- = -- 1 +- = - 1 +- =- = ∫ : integral n convolutio by Response a) ) ( sin t u t F kx x m n ϖ = + : 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 ϖ ϖ ϖ ϖ ϖ , : ICs Satisfying b) ) ( sin t u t F kx x m n ϖ = + : 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 ) ( ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ + = + + + +- = + 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 ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ ϖ 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 +- =...
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Solutions for Test 2 - Solutions for Test 2 1 Problem sin...

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