Question

3. Compute the inverse Laplace transform of \begin{align} F(s) &= \frac{1}{s^4} + \frac{3s}{s^2 + 9} \\ F(s) &= \frac{7}{s} + \frac{6}{s + 4} - \frac{5}{s^2 + 16} \\ F(s) &= \frac{1}{(s - 2)(s + 1)(s - 3)} \\ F(s) &= \frac{s + 2}{s^2(s + 1)} \\ F(s) &= \frac{s + 1}{s(s^2 + 1)} \\ F(s) &= \frac{s^2 + 2s + 4}{(s + 1)(s^2 + 4)^2} \end{align}

          3. Compute the inverse Laplace transform of
\begin{align*} F(s) &= \frac{1}{s^4} + \frac{3s}{s^2 + 9} \\ F(s) &= \frac{7}{s} + \frac{6}{s + 4} - \frac{5}{s^2 + 16} \\ F(s) &= \frac{1}{(s - 2)(s + 1)(s - 3)} \\ F(s) &= \frac{s + 2}{s^2(s + 1)} \\ F(s) &= \frac{s + 1}{s(s^2 + 1)} \\ F(s) &= \frac{s^2 + 2s + 4}{(s + 1)(s^2 + 4)^2} \end{align*}

3. Compute the inverse Laplace transform of

F(s) = (1)/(s^4) + (3s)/(s^2 + 9)
F(s) = (7)/(s) + (6)/(s + 4) - (5)/(s^2 + 16)
F(s) = (1)/((s - 2)(s + 1)(s - 3))
F(s) = (s + 2)/(s^2(s + 1))
F(s) = (s + 1)/(s(s^2 + 1))
F(s) = (s^2 + 2s + 4)/((s + 1)(s^2 + 4)^2)

Added by Jaime C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Adi S

06/05/2023

Step 1

Step 1: To compute the inverse Laplace transform of a given function, we need to find the function in the time domain that corresponds to the given function in the Laplace domain. Show more…

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Answer the full question please and show your steps so I can understand it. If you don't know how to solve the full question leave it for the person who is expert solving this problem. thank you 3. Compute the inverse Laplace transform of 1 35 Fs= 4+ g2+9 7 6 5 Fs= S s +4s2 + 16 1 Fs= (s 2)(s + 1)(s 3) s + 2 F(s)=32(s+1) 3+1 Fs=- =s(s2 +1) s2 + 2s + 4 Fs= (s+12+42