13. 5+25 s³+10s+74
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
In each of Problem 9 through 24, use the linearity of L-1, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function:
Transcribed Image Text:1.
2.
f(t) = L-¹{F(s)}
1
t", n = positive integer
3.
4. t,p>-1
5.
sin at
6.
cos at
7. sinh at
8. cosh at
9. et sin bt
10. et cos bt
11. teat, n positive integer
=
12. uc(t)
13. uc(t)f(t-c)
14. et f(t)
15. Sof(t-1) g(7) dr
16. (t-c)
17. f(n) (t)
18. t" f(t)
F(s) = £{f(t)}
7,8>0
."
s > a
gm+1; 8>0
r(p+1)
8>0
ਕ, 8 > 0
+) 8>0
>
8> |a|
8> |a|
(8-4)³² +6²
8-4
(s-a)² +6²
n!
(s-a) **1'>
"
3
8> a
8> a
e-cs F(s)
F(s-c)
F(s)G(s)
s > a
,s>0
e-cs
snF(s) - s¹-1 f(0) - f(n-1) (0)
(-1)" f(n) (s)
...
Transcribed Image Text:5+25
13-¹+10+74
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