Question

Use partial fractions to find the inverse Laplace transform of the following function. Fis)--3-9s2 Click the icon to view the table of Laplace transforms. (Type an expression using t as the variable.)

Answer 1

Use partial fractions to find inverse Laplace transform F (s) = 2/ s^3 - 9 s^2 L^- 1 [F (s) } = L^- 1 { 2/s^3 - 9s^2 } take partial fraction of 2/s^3 - 9s^2 2/s^3 - 9s^2 = 2/s^2 (s - 9) = A/s + B/s^2 + c/s - 9 implies 2 = As (s - 9) + B (s - 9) + C s^2 put s = 9 implies 2 = c (9)^2 2 = 81 c implies c = 2/81 put s = 0 implies 2 = B (0 - 9) 2 = -9 B implies B = -2/9 2 = As (s - 9) + B (s - 9) + Cs^2n = As^2 - 9As + Bs - 9B + Cs^2 2 = s^2 (A + C) + s (B - 9 A) - 9 B s^2 coefficients: - A + C = 0