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1. f(t) = sin(4t + %3D 3

1. f(t) = sin(4t + %3D 3

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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REFER TO THE LAPLACE TABLE ATTACHED

Table of Laplace Transforms S()={F(s}} F(s) = L{S(1)} S(1)={F(s)} F(s) = £{f(t)} 1. 1 2. e S-a n! Г(р+1) 3. t", n=1,2,3,... 4. ',p>-1 1:3-5.--(2n-1) 2"s*** 5. 6. , n=1,2,3,... 2s a 7. sin(at) 8. cos (at) s+a š+a 2as s-a t sin (at) 10. t cos(at) 9. (s° +a*) (s° +a*)} 2as 2a I1. sin(at)-at cos (at) 12. sin (at)+ at cos(at) (s* +a*)* s(s² -a*) (s' +a') s sin (b)+a cos(b) s +a? (s° +a*) s(s* +3a*) (s* +a*) s cos(b)-a sin(b) 3+a 13. cos(at)-at sin (at) 14. cos (at)+ at sin(at) 15. sin(at +b) 16. cos (at +b) a 17. sinh (at) -a 18. cosh (at) b s-a 19. e sin(bt) 20. cos(bt) (s-a) +b (s-a) +b S-a 21. sinh (bt) 22. e" cosh (bt) (s-a) -b (s-a) -b n! 23. 'e", п%3,2,3,.. 24. f(ct) (s-a) (3-1)g Dirac Delta Function 28. u (1)g(1) u. (1) = u (t-c) 25. 26. Heaviside Function 27. 4, (1)f (1-c) e"F(s) eL{g(1+c)} F(s-c) 30. 1"f (t), n=1,2,3,... (-1)" F" (s) F(s) 29. e“f (t) S F(u)du 32. , s(")dv 31. 33. (t-1)g(r)dt F(s)G(s) 34. f(1+T)= f(t) 1-e s'F(s)-sf (0)-S(0) s'F(s)-s"S(0)-s*/r(0)..-s (0)- f-"(0) 35. f'(t) sF (s)-f(0) 36. Г() 37. f" (1)
Transcribed Image Text:Table of Laplace Transforms S()={F(s}} F(s) = L{S(1)} S(1)={F(s)} F(s) = £{f(t)} 1. 1 2. e S-a n! Г(р+1) 3. t", n=1,2,3,... 4. ',p>-1 1:3-5.--(2n-1) 2"s*** 5. 6. , n=1,2,3,... 2s a 7. sin(at) 8. cos (at) s+a š+a 2as s-a t sin (at) 10. t cos(at) 9. (s° +a*) (s° +a*)} 2as 2a I1. sin(at)-at cos (at) 12. sin (at)+ at cos(at) (s* +a*)* s(s² -a*) (s' +a') s sin (b)+a cos(b) s +a? (s° +a*) s(s* +3a*) (s* +a*) s cos(b)-a sin(b) 3+a 13. cos(at)-at sin (at) 14. cos (at)+ at sin(at) 15. sin(at +b) 16. cos (at +b) a 17. sinh (at) -a 18. cosh (at) b s-a 19. e sin(bt) 20. cos(bt) (s-a) +b (s-a) +b S-a 21. sinh (bt) 22. e" cosh (bt) (s-a) -b (s-a) -b n! 23. 'e", п%3,2,3,.. 24. f(ct) (s-a) (3-1)g Dirac Delta Function 28. u (1)g(1) u. (1) = u (t-c) 25. 26. Heaviside Function 27. 4, (1)f (1-c) e"F(s) eL{g(1+c)} F(s-c) 30. 1"f (t), n=1,2,3,... (-1)" F" (s) F(s) 29. e“f (t) S F(u)du 32. , s(")dv 31. 33. (t-1)g(r)dt F(s)G(s) 34. f(1+T)= f(t) 1-e s'F(s)-sf (0)-S(0) s'F(s)-s"S(0)-s*/r(0)..-s (0)- f-"(0) 35. f'(t) sF (s)-f(0) 36. Г() 37. f" (1)
Find the Laplace transform of 1. f(t) = sin(4t +) 2. f(t) = e-5t cosh(6t) – (9t)"/2 3. f(t) = t cos(5t) + cos(2at) cos (3at) %3D Hint: you may use trigonometric identities.
Transcribed Image Text:Find the Laplace transform of 1. f(t) = sin(4t +) 2. f(t) = e-5t cosh(6t) – (9t)"/2 3. f(t) = t cos(5t) + cos(2at) cos (3at) %3D Hint: you may use trigonometric identities.
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