TABLE OF LAPLACE TRANSFORMS f(r) {f0=F) f() f())=F(s) 1.1 20.eat sinh k (s a)-K 21 21.ea cosh kt s-a 8-a2-2 3. n! napositive integer 22.tsin kt 2ks 2+2乎 4.1~2 限 23.tcoskt 2-k2 2+k2乎 5.72 温 24.sin kt kt cos kt 2k2 2+ 6. 25.sin kt-kt cos kt 2 G2+2乎 7.sin kt 2ks 2+2 26.t sinh kt 2-2呼 8.cos kt 27.t cosh kt s2+k2 2+2 (G2-k乎 22 28-山 1 9.sin2kt 2+4码 a-b (s-0s-b) 10.cos2kt 2+22 sG2+4k码 29.ae-beh a-b (s-a)(s -b) 1 2 11.eat s-a 30.1-cos kt s(2+码 3 12.sinh kt 2-R 3L.k红-sinkt 22+巧 13.cosh kt 32.asin br-bsin at ab(a2-b2) 2+232+b 14.sinh2kt 22 s62-4码 33.cos bi-cos at a2-b2 2+a2s2+b的 15.cosh2kr 32-2k2 34.sin kt sinh kr 23 s(2-4k码 ++40 1 16.tea 35.sin kt cosh kt k(2+2k2) 6- +4 17."eat n! 36.cos kt sinh kt k2-2 (s -ayi, n a positive integer s4+4 k 18.ett sin kt 6-a2+F 37.cos kt cosh kr +4 19.eat cos kt s-a G-a2+k及 38.Jo) 1 VF+元TABLE OF LAPLACE TRANSFORMS f(t) 1. 1 2. t 3. t n n a positive integer 4. t
1/2 5. t 1/2 6. t a 7. sin kt 8. cos kt 9. sin2 kt 10. cos2 kt 11. eat 12. sinh kt 13. cosh kt 14. sinh2kt 15. cosh2kt 16. teat 17. t n eat n a positive integer 18. eat sin kt 19. eat cos kt s
a (s
a) 2 k2 k (s
a) 2 k2 n! (s
a) n1 , 1 (s
a) 2 s2
2k2 s(s2
4k2 ) 2k2 s(s2
4k2 ) s s2
k2 k s2
k2 1 s
a s2 2k2 s(s2 4k2 ) 2k2 s(s2 4k2 ) s s2 k2 k s2 k2 ( 1) s1 , a 
1 1 2s3/2 B  s n! sn1 , 1 s2 1 s
{ f (t)}  F(s) f(t) 20. eat sinh kt 21. eat cosh kt 22. t sin kt 23. t cos kt 24. sin kt kt cos kt 25. sin kt
kt cos kt 26. t sinh kt 27. t cosh kt 28. 29. 30. 1
cos kt 31. kt
sin kt 32. 33. 34. sin kt sinh kt 35. sin kt cosh kt 36. cos kt sinh kt 37. cos kt cosh kt 38. J0(kt) 1 1s2 k2 s3 s4 4k4 k(s2
2k2) s4 4k4 k(s2 2k2) s4 4k4 2k2 s s4 4k4 s (s2 a2 )(s2 b2 ) cos bt
cos at a2
b2 1 (s2 a2 )(s2 b2 ) a sin bt
b sin at ab (a2
b2 ) k3 s2(s2 k2 ) k2 s(s2 k2 ) s (s
a)(s
b) aeat
bebt a
b 1 (s
a)(s
b) eat
ebt a
b s2 k2 (s2
k2 ) 2 2ks (s2
k2 ) 2 2k3 (s2 k2 ) 2 2ks2 (s2 k2 ) 2 s2
k2 (s2 k2 ) 2 2ks (s2 k2 ) 2 s
a (s
a) 2
k2 k (s
a) 2
k2
{ f (t)}  F(s)