Page 22 - LAPLACE TRANSFORM

2.1.1 Table Of Laplace Transforms

No. f(t) F(s) No. f(t) F(s)

1. a a 12. e − at sin ω t ω
2
s ( + as ) + ω 2

2. t ! n 13. e − at cos ω t s + a
n
2
s n 1 + ( + as ) + ω 2

3. t n − 1 1 14. sinh t ω ω
( − 1 )! s n s 2 − ω 2
n
4. e − at 1 15. cosh t ω s

s + a s 2 − ω 2

5. te − at 1 16. e − at sinh t ω ω
2
(s + ) a 2 ( + as ) − ω 2

6. t n e ! n 17. e − at cosh t ω s + a
at
2
( − as ) n + 1 ( + as ) − ω 2

7. t n f . ( ) t d n 18. f ) (t + f ) (t F (s ) F (s )
+
s
( ) 1− n [F ( )] 1 2 1 2
ds n

8. sin t ω ω 19. o ∫ t f ( u) du F( s)
s 2 + ω 2 s

9. cos t ω s 20. f (t − a )u (t − ) a e − as F (s )
s 2 + ω 2

10. t sinω t 2ω s 21. First derivative sY ( ) ys − ( ) 0
(s 2 + ω 2 ) 2 dy ( ) t ' y ,
dt
t
11. t cosω s 2 − ω 2 22. Second derivative s 2 Y ( ) sys − ( ) 0 − ' y ( ) 0
(s 2 + ω 2 ) 2 d 2 y ( ) t ' ' y ,
dt 2

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