f(t) | F(s) |
1 | 1 / s |
t | 1 / s 2 |
t n | n! / s n+1 , (n = 1,2,3...) |
t 1/2 | Pi 1/2 / 2s 3/2 |
t -1/2 | (Pi / s) 1/2 |
e -a t | 1 / (s + a) |
t e -a t | 1 / (s + a) 2 |
sin a t | a / (s 2 + a 2) |
t sin a t | 2 a s / (s 2 + a 2) 2 |
e -at sin b t | b / ( (s + a) 2 + b 2 ) |
cos a t | s / (s 2 + a 2) |
t cos a t | (s 2 - a 2) / (s 2 + a 2) 2 |
e -at cos b t | (s + a) / ( (s + a) 2 + b 2 ) |
sinh a t | a / (s 2 - a 2) |
cosh a t | s / (s 2 - a 2) |
1 - cos a t | a 2 / ( s (s 2 + a 2) ) |
(2 / t)( t - cos a t) | ln [ (s 2 + a 2) / s 2 ] |
(2 / t)( t - cosh a t) | ln [ (s 2 - a 2) / s 2 ] |
(1 / t)( sin a t) | arctan(a / s) |