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ase330m-homework7

# ase330m-homework7 - ASE330MHomework#7(ForExtraCreditOnly...

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ASE 330M – Homework #7 (For Extra Credit Only) Due: December 7 th , 2007 Problem #1: Use the method of partial fraction expansion to identify the inverse Laplace transform of the following functions: (a) () 1 1 Fs ss = + (b) ( ) 3 10 21 0 s e = ++ (c) 2 5 13 s = (d) 2 2 42 24 s s + = Problem #2: Find the Laplace transform of the following functions: (a) () () 1 t f tet = (b) () ( )() ( ) ( ) 3 cos 4 1 2 1 2 t ft e t t t t =+ (c) () () () ( ) ( ) 430 ; 0 1 ; 0 2 xt x x ++= = = ±± ± ± Problem #3: Find the Transfer function, ( ) ref X s X s , for the following systems. Assume all initial conditions are zero. (a) () () () ( ) 3 pr e f x tx t k x t x t += ± (b) () () () () () () ( ) () 0 ; t e f d i r e f x t k x t x t k x t k x x t d τ ± ± where p k , d k , and i k are constants. Let ( ) ( ) ( ) ref ref X sx t = L and ( )( ) X t = L .

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Problem # Described A lineariza approxim Where δθ underdam (a) Fi (b) Fi cl (c) P #4: Consider t d by, ation about t ation of the f () r t θ θθ =− mped, with a ind the transf ind t w lass. rovide a plot the system fr Tt ⎯ ⎯⎯→ ±± he “down” eq form ut δ ⎯⎯⎯→ ± ref , ( TT = natural frequ
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ase330m-homework7 - ASE330MHomework#7(ForExtraCreditOnly...

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