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In each of Problems 9 through 24, use the linearity of L-1, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 30 9.33+25

In each of Problems 9 through 24, use the linearity of L-1, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 30 9.33+25

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 Problems 9 through 24, use the linearity of L-1, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 30 9-33425
Transcribed Image Text:In each of Problems 9 through 24, use the linearity of L-1, partial fraction expansions, and Table 5.3.1 to find the inverse Laplace transform of the given function: 30 9-33425
f(t) = L-¹{F(s)} 1 eat 1. 2. 3. t", n = positive integer 4. t,p>-1 5. sin at 6. cos at 7. sinh at 8. cosh at 9. et sin bt 10. eat cos bt 11. teat, n= positive integer 12. uc (t) 13. uc(t)f(t-c) 14. ect f(t) 15. Söf(t−7)g(7) dr 16. (t-c) 17. f(n) (t) 18. tf(t) F(s) = L{f(t)} },s>0 8-07 n! 8+1) r(p+1) s> 0 a 8²+², 8>0 s > a s> 0 SD+1 " $²+²8>0 a $²², 8> |a| 5²³², 8> |a| b (s-a)² +6² 3 S-a (s-a)² +6² n! (s-a)*+1) e -CS 3 e-cs F(s) F(sc) F(s)G(s) s > a 8 > a s > a s>0 sF(s) s-1 f(0) - (-1) f(n) (s) - f(n-1) (0)
Transcribed Image Text:f(t) = L-¹{F(s)} 1 eat 1. 2. 3. t", n = positive integer 4. t,p>-1 5. sin at 6. cos at 7. sinh at 8. cosh at 9. et sin bt 10. eat cos bt 11. teat, n= positive integer 12. uc (t) 13. uc(t)f(t-c) 14. ect f(t) 15. Söf(t−7)g(7) dr 16. (t-c) 17. f(n) (t) 18. tf(t) F(s) = L{f(t)} },s>0 8-07 n! 8+1) r(p+1) s> 0 a 8²+², 8>0 s > a s> 0 SD+1 " $²+²8>0 a $²², 8> |a| 5²³², 8> |a| b (s-a)² +6² 3 S-a (s-a)² +6² n! (s-a)*+1) e -CS 3 e-cs F(s) F(sc) F(s)G(s) s > a 8 > a s > a s>0 sF(s) s-1 f(0) - (-1) f(n) (s) - f(n-1) (0)
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