MAT514-2008Springv2

# MAT514-2008Springv2 - i i Â r Â t l r Â i Â M A T 5 1 4 I N...

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Unformatted text preview: i i Â¡ r { * Â¿ t . ) l r Â¡ , , ! , i Â¿ M A T 5 1 4 _ I N T R O D U C T I O N T O O R D I N A R Y D I F F E R E N T I A I- E Q U A ' T I O N S F I N A L E X A M- M a y 7 , 2 7 1 [ 1 5 p o i n t s ] G i v e n t h e l i r s t- o r d e r l i n e a r s y s t e m + = l : f t d t L q l ( a ) C o m p u t e t h e e i g e n v a l u e s ; ( b ) F o r e a o h e i g e n v a l u e , c o t n p u t e t h e a s s o c i a t e d e i g e n v e o t o r s ; ( c ) C o m p u t e t h e g e n e r a l s o l u t i o n ; ( d ) S k e t c h t h e p h a s e p o r l r a i t o f t h e s y s t e m . 2 . [ 1 3 p o i n t s l I f a s y s t e m h a s o o m p l e x e i g e n v a l u e s , t h e f u n c t i o n x ( t ) o s o i l l a t e s a b o u t x : w i t h o o n s t a n t p e r i o d , a n d t h e a m p l i t u d e o f s u r : o e s s i v e o s c i l l a t i o n s i s e i t h e r i n o r e a s i n g , d e c r e a s i n g ....
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## This note was uploaded on 06/16/2011 for the course MATH 514 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.

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MAT514-2008Springv2 - i i Â r Â t l r Â i Â M A T 5 1 4 I N...

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