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QUESTION 12 Apply Laplace Inverse to find f(t): s +7 F(s) = 5(52 + 4s +3) Choose the correct answer: L-[F(s)] = f() 1) f(1)
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Q. 12-Ans-) Given FB) = 8 +7 s(8² +48 +3) Breaking into Partial fractions at 847 = 847 = A + B & c & (83+ 4873) 2 ss + 1)(8+3inness & Now taking LEB) Laplace FORD .. FO) = 7o (3) -3.1 St1) +2. 1 6 3 (8+3) 7.234-3226,42 426-3) sek ** <244=1 oo Lapl(2D2 + 3D-2) z = teet (O). Z = ét ezt were f(s = 20² + 30-2 NOW Auxiliary deg. ds. 3. fm) = 0 -> 2m +3m-250 2m2 + 4m-m -2 = 0we know that ref then we will proceed Vr Vixson life. f) vale = e x vas o where (fota) vo is any (FCO) function of . & $80, hPT. - Al et c. 1 202+5D ] 2fol f Ç (-5D) dih 2.Dt + 40²t - - 25 - making 0+401) type 22 } [28]. tg expanding lifal (L =1th +2now uring (0)=-2 ince ) -29 +1 (2 + 1 [+ 7 +0] = -2 = -29, the = -2 + 2 / 5 = 48 25 25 CV honen ® 9-cz 3 +2 2 + 1 2 = 48 ) 2

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