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Find the inverse transform of the given functions: 3s2+5s+5 1. F(s): (s3+8s2+19s+12)(s³) 2. F(s): 5s+3 6S 8 -6 - (5s²+4s+1) s2+7

Find the inverse transform of the given functions: 3s2+5s+5 1. F(s): (s3+8s2+19s+12)(s³) 2. F(s): 5s+3 6S 8 -6 - (5s²+4s+1) s2+7

Advanced Engineering Mathematics
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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Table of Laplace Transforms f(1) = L ' {F(s)} F (s) = L{f(t)} f(1) = L" {F(s)} F(s) = L{f(t)} 1 1 1 2. at 1. S S - a п! Г(р+1) t", n=1,2,3,... 4. t° ,p > -1 sn+1 sP+l 1-3-5...(2n – 1) VT 6. t" , n=1,2,3,... 3 2s? 2" s"+} a sin (at) 8. cos(at) 7. s? +a? s? + a? 2as s² – a? i sin (at) 10. i cos (at) 9. (s² +a* } (s° +a*) 2 2a 2as? 11. sin (at) - at cos (at) sin (at) + at cos (at) 12. (s° +a*} (s² s(s² - a° ) (s° +a*)° +a s(s² + 3a*) За?) 13. cos(at)- at sin(at) 14. cos (at)+ at sin (at) +a s sin (b)+a cos (b) s cos (b)-a sin(b) 15. sin (at + b) 16. cos (at + b) s? + a? s' +a S 17. sinh (at) 18. cosh(at) s² – a? s² - a? S - a 19. e“ sin (bt) 20. e“ cos (bt) 2 (s-a) +b? (s - a)* + +b? S - a e" sinh (bt 21. (ы) e" cosh (bt) 22. (s – a)' – b² (s - a)' –b? n! 23. 1"е", п %3D1,2,3,... 24. f(ct) 1 -F n+1 (s -a)** C u.(1) =u (t -c) 25. 8 (t-c) CS 26. CS e Heaviside Function S Dirac Delta Function 27. и. (1)/ (г—с) 29. e“ f (t) ) F(s-c) u.(t)g (t) t" f (t), n=1,2,3,... e "L{g(t+c}} (-1)" F (s) F(s) +1) ¿ (n) CS e *F (s 28. и. C 1 31. f(1) | F(u) du 32. f(v)dv S T -st 33. f (1-t)g(T)dt F(s)G(s) 34. f(t+T)= f(t) e " f (t) dt -sT 1-e s³F(s)- sf (0)-f'(0) sF (s)- f (0) s"F(s)– s*\f(0)-s*-²f"(0)..-- sf(=-³ (0)– fla-) (0) 35. f'(t) 36. f"(t) 37. f (t) 3. 5.
Transcribed Image Text:Table of Laplace Transforms f(1) = L ' {F(s)} F (s) = L{f(t)} f(1) = L" {F(s)} F(s) = L{f(t)} 1 1 1 2. at 1. S S - a п! Г(р+1) t", n=1,2,3,... 4. t° ,p > -1 sn+1 sP+l 1-3-5...(2n – 1) VT 6. t" , n=1,2,3,... 3 2s? 2" s"+} a sin (at) 8. cos(at) 7. s? +a? s? + a? 2as s² – a? i sin (at) 10. i cos (at) 9. (s² +a* } (s° +a*) 2 2a 2as? 11. sin (at) - at cos (at) sin (at) + at cos (at) 12. (s° +a*} (s² s(s² - a° ) (s° +a*)° +a s(s² + 3a*) За?) 13. cos(at)- at sin(at) 14. cos (at)+ at sin (at) +a s sin (b)+a cos (b) s cos (b)-a sin(b) 15. sin (at + b) 16. cos (at + b) s? + a? s' +a S 17. sinh (at) 18. cosh(at) s² – a? s² - a? S - a 19. e“ sin (bt) 20. e“ cos (bt) 2 (s-a) +b? (s - a)* + +b? S - a e" sinh (bt 21. (ы) e" cosh (bt) 22. (s – a)' – b² (s - a)' –b? n! 23. 1"е", п %3D1,2,3,... 24. f(ct) 1 -F n+1 (s -a)** C u.(1) =u (t -c) 25. 8 (t-c) CS 26. CS e Heaviside Function S Dirac Delta Function 27. и. (1)/ (г—с) 29. e“ f (t) ) F(s-c) u.(t)g (t) t" f (t), n=1,2,3,... e "L{g(t+c}} (-1)" F (s) F(s) +1) ¿ (n) CS e *F (s 28. и. C 1 31. f(1) | F(u) du 32. f(v)dv S T -st 33. f (1-t)g(T)dt F(s)G(s) 34. f(t+T)= f(t) e " f (t) dt -sT 1-e s³F(s)- sf (0)-f'(0) sF (s)- f (0) s"F(s)– s*\f(0)-s*-²f"(0)..-- sf(=-³ (0)– fla-) (0) 35. f'(t) 36. f"(t) 37. f (t) 3. 5.
Find the inverse transform of the given functions: 3s2+5s+5 1. F(s) : (s³+8s²+19s+12)(s³) 5s+3 6s 8 2. F(s) 9- (5s²+4s+1) s2+7 Evaluate using Laplace Transform: f (t) = . tcos 3t dt e-4t
Transcribed Image Text:Find the inverse transform of the given functions: 3s2+5s+5 1. F(s) : (s³+8s²+19s+12)(s³) 5s+3 6s 8 2. F(s) 9- (5s²+4s+1) s2+7 Evaluate using Laplace Transform: f (t) = . tcos 3t dt e-4t
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