Homework 24 Solution

# Homework 24 Solution - Lecture 24 MEEN 357 Homework...

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Lecture 24 MEEN 357 Homework Solution 1 Lecture-24-Homework-Solution.doc RMB 1. Determine the eigenvectors and the eigenvalues of the matrix 11 2 1 526 3 525 2 10 5 10 4 A −− = (24.1) What are the natural frequencies in this case? Solution: The MATLAB script clc clear all A=[1,1,-2,-1;-5,-2,6,3;-5,-2,5,2;10,5,-10,-4] [U,D]=eig(A) Produces the following matrices for U and D 0.1491 0.2981 0.1491 0.2981 0.0000 0.0000 0.4472 0.1491 0.4472 0.1491 0.5914 0.4069 0.2981 0.1491 0.2981 0.1491 0.5772 0.2375 0.7454 0.7454 0.5631 0.8820 ii U −+ ⎡⎤ ⎢⎥ +− = ⎣⎦ (24.2) 10 0 0 01 0 0 00 1 0 0 1 i i D = (24.3) An examination of D shows that the natural frequencies are 1 and 0 . 2. Given the matrix A in (24.1), find the general solution of () () ( ) 1 0 0 2 3 dt At dt ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ == ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ x xx (24.4)

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Lecture 24 MEEN 357 Homework Solution 2 Lecture-24-Homework-Solution.doc RMB 11 2 1 526 3 525 2 10 5 10 4 A −− = (24.5) Use MATLAB as you choose when working this problem.
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Homework 24 Solution - Lecture 24 MEEN 357 Homework...

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