Q.1 Find the Laplace transform for the following 1. t² sin 3t -21 2. t cos³t 3. te sint 5. te ³t sin 3t 6. te cos 2t 7. te ³1 sin² t 2t 9. t (2 sin 3t - 3 cos 3t) 10. te 2¹ (cost-sint) -21 12. te' sin 2t cost 13. te sinh 4t 15. t cos(at - a) 16. (t + sin 2t)² 19. e' sin 4t.cos 2t 18. cosat.sinhat 21. coshat.sin at 24. coshat.cos at 22. cos 3t.cosh 4t 25. t²-3t+5+e²¹² cosht sint -41 27. e4¹3/2 28. e е 30. e2¹ cos2 tcost 31. e²¹ (1+1)² e2t 4. te ³t sin 2t 8. t (2 sin 3t+e +e²¹) 11. e-2¹ (2 tcos2t+sin 2t) 4 14. te3 sinh 2t 17. (t sinh 2t )? 20. e-2¹ (2 cos 3t -3 sin 3t) 23. teat+sin³t 26. cosh at cosbt -31 29. e 32. cosh 4 tsin 3t cos 2t sint e²
Q.1 Find the Laplace transform for the following 1. t² sin 3t -21 2. t cos³t 3. te sint 5. te ³t sin 3t 6. te cos 2t 7. te ³1 sin² t 2t 9. t (2 sin 3t - 3 cos 3t) 10. te 2¹ (cost-sint) -21 12. te' sin 2t cost 13. te sinh 4t 15. t cos(at - a) 16. (t + sin 2t)² 19. e' sin 4t.cos 2t 18. cosat.sinhat 21. coshat.sin at 24. coshat.cos at 22. cos 3t.cosh 4t 25. t²-3t+5+e²¹² cosht sint -41 27. e4¹3/2 28. e е 30. e2¹ cos2 tcost 31. e²¹ (1+1)² e2t 4. te ³t sin 2t 8. t (2 sin 3t+e +e²¹) 11. e-2¹ (2 tcos2t+sin 2t) 4 14. te3 sinh 2t 17. (t sinh 2t )? 20. e-2¹ (2 cos 3t -3 sin 3t) 23. teat+sin³t 26. cosh at cosbt -31 29. e 32. cosh 4 tsin 3t cos 2t sint e²
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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Transcribed Image Text:Q.1 Find the Laplace transform for the following
1. t² sin 3t
2. t cos³t
-21
3. te sint
3t
5. test sin 3t
31
6. te-3t
cos 2t
7. te ³1 sin² t
9. t (2 sin 3t-3 cos 3t)
10. te2¹ (cost - sint)
12. te' sin 2t cost
-21
13. te sinh 4t
15. t cos(at - a)
16. (t+sin 2
t + sin 2t)²
18. cosat.sinhat
19. e' sin 4t.cos2t
21. coshat.sinat
24. coshat.cosat
27. e4¹3/2
22. cos 3t.cosh 4t
25. t²-3t+5+e²¹1.²
-41
28. e
cosht sint
30. e2¹ cos2 tcost
31. e²¹ (1+1)²
4. te ³t sin 2t
8. t (2 sin 3t+e
te²¹)
(2 tcos2t+sin 2t)
11. -e
14. te 3t
sinh 2t
17. (t sinh 2t )
20. e2¹ (2 cos 3t -3 sin 3t)
е
-at
23. the + sin³t
26. cosh at cosbt
-31
29. e
32.
cosh 4 tsin 3t
cos 2t sint
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