me375_fa10_hwk03

# me375_fa10_hwk03 - conditions of x = and x = x 16 x = 4 t d...

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ME 375 – Fall 2010 Homework No. 3 Due: Friday, September 17 Problem No. 1 (30%) a) For u t ( ) shown below, determine the Laplace transform U s ( ) = L u t ( ) ! " # \$ . b) For u t ( ) = 3 sin 4 t + 20 ( ) , determine the Laplace transform U s ( ) = u t ( ) ! " # \$ . c) If Y s ( ) = s + 3 6 s 2 + 5 s + 4 is the Laplace transform of y t ( ) , what is y t = 0 ( ) ? d) If Y s ( ) = s + 3 6 s 2 + 5 s + 4 is the Laplace transform of y t ( ) , what is the Laplace transform of e ! 2 t y t ( ) ? t u t ( ) 2 10 0

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Problem No. 2 (40%) a) Determine the solution x t ( ) for the following differential equation with the initial conditions of x 0 ( ) = 6 : 5 ! x + 10 x = 15 b) Determine the solution x t ( ) for the following differential equation with the initial conditions of x 0 ( ) = 0 and ! x 0 ( ) = 2 : !! x + 9 x = 10 c) Determine the solution x t ( ) for the following differential equation with the initial
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Unformatted text preview: conditions of x ( ) = and ! x ( ) = : !! x + 16 x = 4 t d) Determine the solution x t ( ) for the following differential equation with the initial conditions of x ( ) = and ! x ( ) = : !! x + 64 x = sin 4 t ( ) e) The Laplace transform of the response x t ( ) is known to be: X s ( ) = s 2 + 4 s s 2 + 9 ( ) . Determine the response x t ( ) . Problem No. 3 (30%) Consider the following input-output system: 5 !! y + 80 ! y + 500 y = 50 u ! 12.5 !! u with u t ( ) being the input and y t ( ) being the output. a) Determine the transfer function G s ( ) = Y s ( ) U s ( ) . b) Determine the poles and zeros of your transfer function from a) above....
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me375_fa10_hwk03 - conditions of x = and x = x 16 x = 4 t d...

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