Question

Inverse Laplace Transform: Q2. Find the inverse Laplace transform for each of the following functions: a. F(s)= 1 / ((s+1)(s^2-1)) b. G(s)= (2s+3) / (s^2+4s+13) c. Y(s)= e^(-3s) / (s-2) d. H(s) = (1 + e^(-2s)) / (s^2+6)

          Inverse Laplace Transform:

Q2. Find the inverse Laplace transform for each of the following functions:

a. F(s)= 1 / ((s+1)(s^2-1))

b. G(s)= (2s+3) / (s^2+4s+13)

c. Y(s)= e^(-3s) / (s-2)

d. H(s) = (1 + e^(-2s)) / (s^2+6)

Added by Kelly W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

04/05/2023

Step 1

We can do this by performing partial fraction decomposition. F(s) = \frac{(s+1)(s^2+1)}{2s+3} = \frac{A}{s} + \frac{B}{2s+3} + \frac{Cs+D}{s^2+1} Now, we need to find the constants A, B, C, and D. Multiplying both sides by the common denominator (2s+3)(s^2+1), Show more…

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Inverse Laplace Transform: Q2. Find the inverse Laplace transform for each of the following functions: a. F(s) = 1 / ((s+1)(s^2-1)) b. G(s) = (2s+3) / (s^2+4s+13) c. Y(s) = e^(-3s) / (s-2) d. H(s) = (1 + e^(-2s)) / (s^2+6)