Apply the translation theorem to find the inverse Laplace transform of the following function. 9S+12 F(s) = S²-85+41 L₁₁ {F(s)} = (please enter an expression using t as the variable.
Apply the translation theorem to find the inverse Laplace transform of the following function. 9S+12 F(s) = S²-85+41 L₁₁ {F(s)} = (please enter an expression using t as the variable.
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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Question
![Apply the translation theorem to find the
inverse Laplace transform of the following function.
9s+12
F(s) =
S²-85+41
L₁' {F(s)} =
Table of Laplace transforms
f(t)=L¹{F(s)} L{f(t)} = F(s)
1
1
(s > 0)
S
1
5²
n!
t
ta
eat
n+1
s
[(a+1)
n+1
s'
1
s-a
(s > 0)
(s> 0)
(s>0)
(s>a)
f(t)=L¹{F(s)}
cos kt
sin kt
cosh kt
sinh kt
(please enter an expression
using t as the variable)
eatin
L{f(t)} = F(s)
S
s²+k²
k
s²+k²
S
s²-K²
k
2
s-k
n!
(s-a)+1
(s > 0)
(s > 0)
(s> |k|)
(s> |kl)
(s>a)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46890c96-3b8c-4ea6-bb6b-a8358fcd3c49%2Fe1b4db67-7bcb-4f51-8c3f-916c28d350f6%2Fkf6hj0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Apply the translation theorem to find the
inverse Laplace transform of the following function.
9s+12
F(s) =
S²-85+41
L₁' {F(s)} =
Table of Laplace transforms
f(t)=L¹{F(s)} L{f(t)} = F(s)
1
1
(s > 0)
S
1
5²
n!
t
ta
eat
n+1
s
[(a+1)
n+1
s'
1
s-a
(s > 0)
(s> 0)
(s>0)
(s>a)
f(t)=L¹{F(s)}
cos kt
sin kt
cosh kt
sinh kt
(please enter an expression
using t as the variable)
eatin
L{f(t)} = F(s)
S
s²+k²
k
s²+k²
S
s²-K²
k
2
s-k
n!
(s-a)+1
(s > 0)
(s > 0)
(s> |k|)
(s> |kl)
(s>a)
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