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Unformatted text preview: 1 Frequency Response Analysis Frequency Response Analysis Analytical Expression for Frequency response Given that a linear timeinvariant system is represented by a transfer function of G ( s ). Let the system input be a sinusoidal motion , i.e., x ( t ) = X sin( t ), where X is the amplitude and is the frequency of the input signal . The Laplace transform of x ( t ) is given by 2 2 ) ( + = s X s X 2 Analytical Expression for Frequency Response Thus, one has the system output as C ( s ) 2 2 ) ( ) ( ) ( ) ( + = = s X s G s R s G s C ( ) ( ) j s j s X s G s C + = ) ( ) ( 3 Analytical Expression for Frequency Response Performing a partial fraction expansion on the above equation ) ( from erms fraction t Partial ) ( 2 1 s G j s K j s K s C + + + = [ ] ) ( 2 ) ( ) ( ) ( 1 j G j X s G j s X S G j s K j s j s = + = = = = [ ] ) ( 2 ) ( ) ( ) ( 2 j G j X s G j s X S G j s K j s j s = = + = = = 4 Analytical Expression for Frequency Response Please note that G ( j ) and G ( j ) are complex numbers. By using the Eulers formula , these two...
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This note was uploaded on 05/26/2010 for the course ME 5659 taught by Professor Jalili during the Spring '10 term at Northeastern.
 Spring '10
 Jalili
 Mechatronics

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