2018_CLASS_TEST_2_MEMO.pdf - EERI 224 MEMO Class test 2 VRAAG 1 QUESTION 1 Vind G(s deur gebruik te maak van die volgende g(t Find G(s by making use of

2018_CLASS_TEST_2_MEMO.pdf - EERI 224 MEMO Class test 2...

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EERI 224 MEMO Class test 2 - 06/08/2018 VRAAG 1 / QUESTION 1 Vind G(s) deur gebruik te maak van die volgende g(t) / Find G(s) by making use of the following g(t): (a) (b) (Homework problem 12.24 b) Let therefor, 12 te 30 t g ( t ) = 12 te 30 t G ( s ) = { g ( t )} = 12 ( s + 30) 2 t 0 e ax sin ω x d x g ( x ) = t 0 e ax sin ω xd x and g 1 ( x ) = e ax sin ω x and let { g ( x )} = G 1 ( s ) s G 1 ( s ) = ω ( s + a ) 2 + ω 2 G ( s ) = ω s [ ( s + a ) 2 + ω 2 ] 1
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(c) (Homework problem 12.24 a) VRAAG 2 / QUESTION 2 Beantwoord die onderstaande vrae gegewe die volgende uitdrukking: / Answer the questions below given the following expression: (a) Is F(s) ’n betaamlik rasionele funksie van s? Gee ’n rede vir jou antwoord / Is F(s) a proper rational function of s? Give a reason for your answer. (2) Yes, the function F(s) is a proper rational function. The reason be: m > n (b) Watter tipe wortels het die noemer van F(s)? / Which types of roots does the denominator of F(s) have? (2) The function F(s) has: (1) Real and distinct root, and (2) 2x Complex and distinct roots. d dt ( e at cos ω t ) g ( t ) = d dt g 1 ( t ) where g 1 ( t ) = e at cos ω t G ( s ) = sG 1 ( s ) g (0 ) G 1 ( s ) = s + a ( s + a ) 2 + ω 2 G ( s ) = s ( s + a ) ( s + a ) 2 + ω 2 1 = a 2 as ω 2 ( s + a ) 2 + ω 2 F ( s ) = 15( s 2 + 125) ( s + 5)( s + 5 j 12)( s + 5 + j 12) 2
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(c) Ontbind F(s) in parsiële breuke en bepaal die waarde van elke term se koëffisiënt. /
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