ME581_Assignment04

ME581_Assignment04 - ME 581 Assignment #4 Eigenvalue...

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ME 581 Assignment #4 – Eigenvalue problem In the following questions show the derivations that you used to write your programs. 1. For the following matrices: ( do manual calculations ) a. = 3 0 0 1 2 0 4 2 1 ] [ A b. = 1 1 4 1 ] [ B Calculate the determinant. Calculate the eigenvalues. Calculate the eigenvectors. 2. For the system described by the following differential equation: ( do manual calculations ) = + 0 0 0 1 1 0 1 2 1 0 1 2 100 1 0 0 0 1 0 0 0 1 10 3 2 1 3 2 1 x x x x x x a. Find the natural frequencies and mode shapes (eigenvectors). b. If 0 ) 0 ( ) 0 ( ) 0 ( 3 2 1 = = = x x x and 1 . 0 ) 0 ( ) 0 ( ) 0 ( 3 2 1 = = = x x x , find ) ( 1 t x , ) ( 2 t x and ) ( 3 t x . 3.
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