Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: 1 s+o(e-as-e-bs) where a, b, and o are constants. F(s) =
Compute the inverse Laplace transform f(t) = L−¹[F(s)] of the following function: 1 s+o(e-as-e-bs) where a, b, and o are constants. F(s) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function:
1
s+o
F(s) =
-as
- e-bs)
where a, b, and o are constants.
Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] =
e-saF (s), which implies that
f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd23cf25f-e0e1-420e-8dcb-8ea8662c7deb%2Fce257941-09f3-4e43-9858-fd6ee56bc14c%2Fqjpodhg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Compute the inverse Laplace transform f(t) = L-¹[F(s)] of the following function:
1
s+o
F(s) =
-as
- e-bs)
where a, b, and o are constants.
Hint: Recall that the following property holds for translated functions L[f(t-a)H(ta)] =
e-saF (s), which implies that
f(t) = L-1¹[e-sa F (s)] = f(t— a)H(t − x)
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