sln11 - EAS4510 Homework#11 Solution#1 Given 4 4n 2 U xx U...

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EAS4510 Homework #11 Solution #1) Given: () ( ) 00 0 42 2 2 2 2 2 1,2 40 0 4 2 xx yy xx yy xx nU U UU U bc bb c λλ αλ αα α +− + = = ++ = −± = (i) 1,2 i Î i λ =± ± Î = 0.7071 + 0.7071i 0.7071 - 0.7071i -0.7071 - 0.7071i -0.7071 + 0.7071i (ii) 1,2 49 i Î i = ±± Î = 2.6314 + 1.7101i 2.6314 - 1.7101i -2.6314 - 1.7101i -2.6314 + 1.7101i (iii) 1.7101 + 2.6314i 1.7101 - 2.6314i -1.7101 - 2.6314i -1.7101 + 2.6314i (iv) 0 + 2.0000i 0 + 2.0000i 0 - 2.0000i 0 - 2.0000i (v) 2 2 -2 -2 (vi) 2 3 -2 -3 (vii) 0 + 2.0000i 3 0 - 2.0000i -3 (viii) 0 + 2.0000i 0 + 3.0000i 0 - 2.0000i 0 - 3.0000i #2) Put in state space form for first order differential equations. a) 1 2 3 4 x x x x x y x y = = = = ± ± Î 11 2 22 33 44 01 0 0 30 0 0 0 0 1 0 0 xx n ⎡⎤ ⎢⎥ = = ⎣⎦ ± ± ± ± Î 000 0 100 10 0 0 3 0 0 0 3 0 0 det 0 det det 0 0 001 0 0 1 0 000 0 0 0 nn IA ⎛⎞ ⎜⎟ −= = = ⎝⎠ Î 2 03 n =− Î 0,0, 3 n
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b) 11 2 22 33 44 01 0 0 30 0 2 0 00 0 1 02 0 0 xx nn n ⎡⎤ ⎢⎥ −− == ⎣⎦ ± ± ± ± Î () 000 0 1 0 0 0 3 0 0 2 3 0 2 det 0 det det 0 0 0 0 1 0 0 1 0 2 0 0 0 2 0 IA λλ λ ⎛⎞ ⎜⎟ −= = =
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This note was uploaded on 08/26/2008 for the course EAS 4510 taught by Professor Fitz-coy during the Spring '05 term at University of Florida.

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sln11 - EAS4510 Homework#11 Solution#1 Given 4 4n 2 U xx U...

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