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Unformatted text preview: in terms of a magnitude and a direction: 1 G ( j ) = M ( ) e j ( ) where M ( ) =  G ( j ) and ( ) = G ( j ). Since all complex zeros and poles of G ( s ) come in  conjugate pairs (as they do for any reallife transfer function): G ( j ) = M ( ) e j ( ) Now substitute again into the equation for c ss : A 2 j ( M ( ) e j ( t + ( )) + M ( ) e j ( t + ( ) ) c ss = But e j = cos + j sin and e j = cos j sin , so we get: A c ss = (2 jM ( ) sin( t + ( ))) 2 j = AM ( ) sin( t + ( )) A sin( t )AM ( ) sin( t + ( )) G ( s ) 2...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
 Fall '03
 willcox
 Aeronautics, Astronautics

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