# quiz1 - L H t-8 t-8 = e-8 s L t = e-8 s s 2 From the same...

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Solution for Quiz 2 Find the Laplace transform of the function f ( t ) given by f ( t ) = ( 0 , 0 t < 8 , 5 t, t 8 . First we express this function in terms of the Heaviside function, f ( t ) = 5 tH ( t - 8) . Then we evaluate the Laplace transform: L [ f ] = L [5 tH ( t - 8)] = 5 L [ H ( t - 8) t ] = 5 L [ H ( t - 8)( t - 8 + 8)] = 5 L [ H ( t - 8)( t - 8) + 8 H ( t - 8)] = 5 L [ H ( t - 8)( t - 8)] + 40 L [ H ( t - 8)] . From Second Shifting Theorem,
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Unformatted text preview: L [ H ( t-8)( t-8)] = e-8 s L [ t ] = e-8 s s 2 . From the same theorem, or from Example 3.11 of the book, we have L [ H ( t-8)] = e-8 s L [1] = e-8 s s . Therefore, L [ f ] = 5 e-8 s s 2 + 40 e-8 s s . 1...
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## This note was uploaded on 01/12/2010 for the course MATH 421 taught by Professor Nataliakomarova during the Winter '07 term at San Jose State.

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