Question

Questions 7-12: Find the inverse Laplace transform of the following. 1) F(s) = s+7 e +2)e(s+8) 10.) F(s)+2 s2 +3s +6 2s + 22 8.) F(s)--s428- 11.) Fo) 4s+13 12s +108s2 +552s +1008 +12s +107s +426s+754 34s2 +119s+71 12.) F(s)

Answer 1

F(s) = s + 7/s^2 = 1/s + 7/s^2 Apply 1.L.T F(t) = (1 + 7t)u(t) 8) F(s) = s^2 + 3s + 6/s^2(s + 2) = A/s + B/s^2 + C/s + 2 s^2 + 3s + 6 = As(s + 2)+ B(s + 2)+ cs^2 - (1) put s = 0 in (1) 6 = 0 + B(2) + 0 rightarrow B = 3 put s = -2 in(1) (- 2)^2 + 3(- 2ightarrow c = 1 compare s^2 co - efficient in(1) 1 = A + C rightarrow A = 0 F(s) = 3/s^2 + 1/s + 2 Apply 2.L.T f(t) = (3t + e^- 2t)u(t) a) F(s) = 34 s^2 + 119s + 71/2(s + 1/2)(s + 3)(s + 1) F(s) = 2[34s^2 + 119s + 71/(s + 1/2)(s + 1)(s + 3)] = A/s + 1/2 + B/s + 1 + 1/s + 3 34 s^2 + 119 s + 71 = A(s + 1)(s + 3)+ B(s + 1/2)(s + 3) + C(s + 1)(s + 1/2) - (2) put s = -1/2 in (2) 8.5 - 59.5 + 71 = A(1/2)(5/2)+ 0 + 0 A = 16 \r\n put s = -1 in (2) 34 - 119 + 71 = 0 + B(- 1/2)(2) + 0 B = 14 put s = -3 in(2)

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