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In each of Problem 9 through 24, use the linearity of L¹, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function: 23- -28²-68-6 (s²+2s+2) s²

In each of Problem 9 through 24, use the linearity of L¹, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function: 23- -28²-68-6 (s²+2s+2) s²

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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In each of Problem 9 through 24, use the linearity of L¹, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function: 23. -28²-68-6 (s²+2s+2)s²
Transcribed Image Text:In each of Problem 9 through 24, use the linearity of L¹, partial fraction expression, and Table 5.3.1 to find the inverse Laplace transform of the given function: 23. -28²-68-6 (s²+2s+2)s²
1. 2. f(t) = -¹{F(s)} 1 eat t", n = positive integer 3. 4. t,p>-1 5. sin at 6. cos at sinh at 7. 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. e f(t) 15. ff(t-1) 9(7) dr 16. (t-c) 17. f(n) (t) 18 the f(t) F(s) = L{f(t)} 1,8>0 s>a g+18>0 r(p+1) 8> 0 8>0 8>0 8> lal 8> |a| (5-4)² +52) > a 8 (5-4)² +6² 8>a + + s> a (s-a) **I' e, s>0 e-cs F(s) F(s-c) F(s)G(s) s" F(s)-8"-1f(0) - (-1)^ f(n) (s) - f(n-1) (0)
Transcribed Image Text:1. 2. f(t) = -¹{F(s)} 1 eat t", n = positive integer 3. 4. t,p>-1 5. sin at 6. cos at sinh at 7. 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. e f(t) 15. ff(t-1) 9(7) dr 16. (t-c) 17. f(n) (t) 18 the f(t) F(s) = L{f(t)} 1,8>0 s>a g+18>0 r(p+1) 8> 0 8>0 8>0 8> lal 8> |a| (5-4)² +52) > a 8 (5-4)² +6² 8>a + + s> a (s-a) **I' e, s>0 e-cs F(s) F(s-c) F(s)G(s) s" F(s)-8"-1f(0) - (-1)^ f(n) (s) - f(n-1) (0)
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