2:12 РМ Tuе Apr 1384%FIU SPRING 2021HomeInsertDrawViewClass NotebookA Text ModeLasso SelectInsert Space2. Use Table 9.1 to find the inwerse Laplace transform L" ŹFIS1},whereFis) =S2 -48-4Table of Laplace Transformsf(1)= £*{F(s)}_F(s) = L{f(}S() =L*{F(s}}F(s)= 2{f(1)}1.12. еаS-ar(p+1)n!3.", п%31,2,3,...4.",p> -11-3-5..-(2n –1)Va2"s"}5. Vi6. 1", n=1,2,3,...2sa7.sin (at)8. cos(at)g² +a?g² -a?2as9. t sin(at)10. i cos(at)(s* +a*)°2a2as?11. sin(at)- at cos (at)12. sin(at)+ at cos(at)s(s² -a')13. cos(at)– at sin (at)14. cos(at)+at sin(at)(s* +a*)'s sin (b)+a cos(b)g² +a²16. cos(at +b)s cos (b)– a sin(b)s² +a?15. sin(at + b)a17. sinh(at)18. cosh(at)S-a19. е" sin (bl)20. e" сos(b)(s-a) +b?(s-a) +b?S-a21. e" sinh(bt)22. e" cosh(bt)(s-a) -b²(s-a) -b²n!23. "е", пъ1,2,3,...(s-a)*24. f(ct)u. (1) = u(t-c)8(t-c)e25.Heaviside Function26.Dirac Delta Function28. и. ():()ee "£{s(++c}}(-1)" fl^ (s)F(s)27. u. (1)f (1-c)e"F(s)F(s-c)29. e“ f (t)30. "f(0), п-31,2,3,...32. f(v)dv31.33. S(1-1)g(+)dtF(s)G(s)34. f(t+T)= f (t)1-e-s7sF(s)-f(0)s'F(s)-sf (0)- f'(0)35. f'(t)37. fl" (1)36. f"(t)s'F(s)-s"!f(0)-s*²f"(0)..--sple-9 (0)– fl-) (0)

Answered: Image /qna-images/answer/178f5c04-807d-4dc4-af93-819e0daad1a1.jpg

2. use Table 9.1 to find the inverse Laplace transform L-" {FlS1}, where Fis) = 82 -46-4 Table of Laplace Transforms S(1) = L*{F(s)}_F(s) = L{f(!} S(1) = L*{F(s}} F(s) =£{S(1)} 1. 1 2. e S-a n! r(p+1) 3. ", n=1,2,3,... 4. ',p>-1 6. , n=1,2,3,.. 1-3-5.-(2n –1)/« 5. a sin (at) 8. cos(at) 7. 2as s-a 9. tsin(at) 10. t cos(at) 2a 2as 11. sin(ar)– at cos(at) 12. sin(at)+at cos(at) 13. cos(at) – at sin (at) 14. cos(at)+ at sin(at) 15. sin(at + b) ssin (b) + acos(b) 16. cos(at +b) s cos(b) – a sin(b) 17. sinh(at) 18. cosh(at) S-a 19. e" sin(bt) (s-a) +b² | 20. e" cos(bt) (s-a) +b² S-a 21. e“ sinh(bt) 22. " cosh(br) (s-a) -b² (s-a)* -b² n! 23. "e", n=1,2,3,... | 24. S(ct) (s-a)™ 25. 4.(1) = «(1 -c) 8(1-c) e Heaviside Function 27. u.(1)S(1-c) 29. e"f(1) 26. Dirac Delta Function 28. и. ():() 30. "S(1), n= 1,2,3,... e"e{g(t+c)} (-1)" F®) (s) F(s) e"F(s) F(s-c) 31. 10) 32. S(^)dv 33. s(1-1)8(t)dt F(s)G(s) 34. S(1+T)= f(1) 1-e 36. S"(1) 35. Г() 37. f(t) sF(s)- f(0) s*F(s)-sf (0)– f'(0) s'F(s)-s*!f(0)-s*?s (0)..--sgte"(0)- ~-"(0)

2. use Table 9.1 to find the inverse Laplace transform L-" {FlS1}, where Fis) = 82 -46-4 Table of Laplace Transforms S(1) = L{F(s)}_F(s) = L{f(!} S(1) = L{F(s}} F(s) =£{S(1)} 1. 1 2. e S-a n! r(p+1) 3. ", n=1,2,3,... 4. ',p>-1 6. , n=1,2,3,.. 1-3-5.-(2n –1)/« 5. a sin (at) 8. cos(at) 7. 2as s-a 9. tsin(at) 10. t cos(at) 2a 2as 11. sin(ar)– at cos(at) 12. sin(at)+at cos(at) 13. cos(at) – at sin (at) 14. cos(at)+ at sin(at) 15. sin(at + b) ssin (b) + acos(b) 16. cos(at +b) s cos(b) – a sin(b) 17. sinh(at) 18. cosh(at) S-a 19. e" sin(bt) (s-a) +b² | 20. e" cos(bt) (s-a) +b² S-a 21. e“ sinh(bt) 22. " cosh(br) (s-a) -b² (s-a)* -b² n! 23. "e", n=1,2,3,... | 24. S(ct) (s-a)™ 25. 4.(1) = «(1 -c) 8(1-c) e Heaviside Function 27. u.(1)S(1-c) 29. e"f(1) 26. Dirac Delta Function 28. и. ():() 30. "S(1), n= 1,2,3,... e"e{g(t+c)} (-1)" F®) (s) F(s) e"F(s) F(s-c) 31. 10) 32. S(^)dv 33. s(1-1)8(t)dt F(s)G(s) 34. S(1+T)= f(1) 1-e 36. S"(1) 35. Г() 37. f(t) sF(s)- f(0) sF(s)-sf (0)– f'(0) s'F(s)-s!f(0)-s*?s (0)..--sgte"(0)- ~-"(0)

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

2:12 РМ Tuе Apr 13
84%
FIU SPRING 2021
Home
Insert
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Class Notebook
A Text Mode
Lasso Select
Insert Space
2. Use Table 9.1 to find the inwerse Laplace transform L" ŹFIS1},
where
Fis) =
S2 -48-4
Table of Laplace Transforms
f(1)= £*{F(s)}_F(s) = L{f(}
S() =L*{F(s}}
F(s)= 2{f(1)}
1.
1
2. еа
S-a
r(p+1)
n!
3.
", п%31,2,3,...
4.
",p> -1
1-3-5..-(2n –1)Va
2"s"}
5. Vi
6. 1", n=1,2,3,...
2s
a
7.
sin (at)
8. cos(at)
g² +a?
g² -a?
2as
9. t sin(at)
10. i cos(at)
(s* +a*)°
2a
2as?
11. sin(at)- at cos (at)
12. sin(at)+ at cos(at)
s(s² -a')
13. cos(at)– at sin (at)
14. cos(at)+at sin(at)
(s* +a*)'
s sin (b)+a cos(b)
g² +a²
16. cos(at +b)
s cos (b)– a sin(b)
s² +a?
15. sin(at + b)
a
17. sinh(at)
18. cosh(at)
S-a
19. е" sin (bl)
20. e" сos(b)
(s-a) +b?
(s-a) +b?
S-a
21. e" sinh(bt)
22. e" cosh(bt)
(s-a) -b²
(s-a) -b²
n!
23. "е", пъ1,2,3,...
(s-a)*
24. f(ct)
u. (1) = u(t-c)
8(t-c)
e
25.
Heaviside Function
26.
Dirac Delta Function
28. и. ():()
e
e "£{s(++c}}
(-1)" fl^ (s)
F(s)
27. u. (1)f (1-c)
e"F(s)
F(s-c)
29. e“ f (t)
30. "f(0), п-31,2,3,...
32. f(v)dv
31.
33. S(1-1)g(+)dt
F(s)G(s)
34. f(t+T)= f (t)
1-e-s7
sF(s)-f(0)
s'F(s)-sf (0)- f'(0)
35. f'(t)
37. fl" (1)
36. f"(t)
s'F(s)-s"!f(0)-s*²f"(0)..--sple-9 (0)– fl-) (0)

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