2018_CLASS_TEST_1_LAPLACE_MEMO.pdf - EERI 224 MEMO Class test 1 VRAAG 1 QUESTION 1 Gegewe dat Given that ℒ{f(t = ∞ ∫0 − f(t)e −st dt F(s =

# 2018_CLASS_TEST_1_LAPLACE_MEMO.pdf - EERI 224 MEMO Class...

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EERI 224 MEMO Class test 1 - 23/7/2018 VRAAG 1 / QUESTION 1 Gegewe dat / Given that: (a) Unit step function (b) The function t Make use of integration by parts, where { f ( t ) } = 0 f ( t ) e st dt F ( s ) = { f ( t ) } u ( t ) = { 1 for t > 0 0 for t < 0 { f ( t ) } = 0 f ( t ) e st dt = 0 1. e st dt = 1 s [ e st ] 0 = 1 s { f ( t ) } = 0 f ( t ) e st dt = 0 t . e st dt uv = uv u v 1
Therefor, we choose u and v so that (c) (d) There are two ways to derive the Laplace transform for sin: OPTION 1: Using Euler’s identity OPTION 2: Using integration by parts (x2) u = t and v = e st u = 1 and v = 1 s e st 0 t . e st dt = t . 1 s e st 0 0 1. 1 s e st dt = te st s 0 + 1 s 0 e st dt = [0] + 1 s [ 1 s e st ] 0 = 1 s [ 1 s ( 0 1 )] = 1 s 2 { f ( t ) } = 0 f ( t ) e st dt = 0 e at . e st dt = 0 e ( s + a ) t dt = 1 s + a e ( s + a ) t 0 = 1 s + a ( 0 1 ) = 1 s + a sin( ω t ) = e j ω t e j ω t 2 j 2
OPTION 1: OPTION 2:

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