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
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Chapter2: Second-order Linear Odes
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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)
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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