Question

Find the inverse Laplace transform of F(s) = frac{5e^{-6s}}{s^2 + 64} f(t) = (Notation: write u(t-c) for the Heaviside step function u_c(t) with step at t = c.)

          Find the inverse Laplace transform of
F(s) = frac{5e^{-6s}}{s^2 + 64}
f(t) = 
(Notation: write u(t-c) for the Heaviside step function u_c(t) with step at t = c.)

$Find the inverse Laplace transform of F(s) = frac5e^-6ss^2 + 64 f(t) = (Notation: write u(t-c) for the Heaviside step function uc(t) with step at t = c.)$

Added by Edward H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/02/2023

Step 1

We can use the table of Laplace transforms to find that: L^-1{s^2} = t^2 L^-1{64} = 64δ(t) where δ(t) is the Dirac delta function. Therefore, we have: L^-1{F(s)} = L^-1{s^2 + 64} = L^-1{s^2} + L^-1{64} = t^2 + 64δ(t) Show more…

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