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ECE633F09_HW6solutions

# ECE633F09_HW6solutions - = This is the html version of the...

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β β = β 2/11/2010 11:44:28 AM https://mail.google.com/mail/?shva=1#inbox This is the html version of the file http://www.ece.unh.edu/courses/ece633/pdf/ECE633F09_HW6solutions.pdf . Google automatically generates html versions of documents as we crawl the web. Page 1 ECE 633 Signals and Systems I , Fall 2009 Homework 6 Solutions From : Linear Systems and Signals , 2 nd ed . B . P . Lathi , Oxford University Press , 2005 . 2 . 5 - 1 Use the classical method to solve ( ) ( ) ( ) ( ) 2 7 12 2 D D y t D x t + + = + for initial conditions of ( ) 0 y + = , ( ) 1 y + = , and input ( x t of ( a ) ( u t ( b ) ( ) e u t ( c ) ( ) e u t The natural response is ( ) 1 t t y t ke ke = + . ( a ) ( ) y t φ β = ( ) ( ) 2 0 7 12 2 1 D D D β + + = + 0 1 / 6 β = ( ) ( ) ( ) 3 1 1 / 6 t t y t y t t k e k e φ = + = + + ( ) 3 4 3 4 t t y t ke ke = ( ) ( ) 2 1 2 2 2 2 0 1 / 6 3 1 / 2 1 1 3 4 2 3 0 3 4 k k k k k k k k k + + = = + + = + + ˰ ˰ = ˰ = = = = ( ) 1 1 1 for 0 3 2 6 t t y t e e t = + ( b ) ( t y t e φ β = ( ) ( ) 7 12 2 t t t D e De e De e β + + = + ( ) ( ) ( ) ( ) 7 12 2 1 12 1 2 1 / 6 t t t t e e e e e β β β + = + ˰ + = + ˰ = ( ) ( ) ( ) ( ) 3 1 2 1 1 0 6 6 1 1

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