# m238sp05t4s - Mathematics 238 test four solutions Friday,...

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Mathematics 238 test four solutions Friday, June 10, 2005 please tell me about any errors 1 . Find the function which corresponds to each Laplace transform: ( a ) 2 ( s + 4) 3 apply the translation principle: function transform t 2 2! s 3 = 2 s 3 t 2 e - 4 t 2 ( s + 4) 3 Therefore L - 1 ± 2 ( s + 4) 3 ² = t 2 e - 4 t ( b ) L - 1 ³ s + 3 s 2 - s - 6 ´ = L - 1 ± s + 3 ( s - 3)( s + 2) ² partial fractions = L - 1 ± 6 5 s - 3 + - 1 5 s + 2 ² = 6 5 e 3 t - 1 5 e - 2 t ( c ) 6 e - 2 s s 2 + 9 apply the 2 nd translation principle: function transform 2 sin 3 t 2 · 3 s 2 + 3 2 u 2 ( t ) (2 sin 3( t - 2)) 2 · 3 s 2 + 3 2 · e - 2 s Therefore L - 1 ± 6 e - 2 s s 2 + 9 ² = 2 u 2 ( t ) sin 3( t - 2) 2 . Simplify each of the following: ( a ) Z 0 µ e - 3 t cos 4 t e - st dt = L n e - 3 t cos 4 t o = s + 3 ( s + 3) 2 + 4 2 ( b ) Use the convolution theorem L n t 2 * t 3 o = L n t 2 o ·L n t 3 o = 2 s 3 · 6 s 4 = 12 s 7 = L ³ 1 60 t 6 ´ Therefore t 2 * t 3 = 1 60 t 6

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page two 3 . Sketch the graph of the function f ( t ) = 3( u 2 ( t ) - u 4 ( t
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## This note was uploaded on 11/01/2010 for the course ENGINEERIN PHYS222 taught by Professor Ewqfqw during the Spring '09 term at University of Washington.

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m238sp05t4s - Mathematics 238 test four solutions Friday,...

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