| Constant |
1 |
$\dfrac{1}{s}$ |
| Linear |
$t$ |
$\dfrac{1}{s^2}$ |
| Power |
$t^n$ |
$\dfrac{n!}{s^{n+1}}$ |
| Exponent |
$e^at$ |
$\dfrac{1}{s-a}$ |
| Sine |
$sin~at$ |
$\dfrac{a}{s^2+a^2}$ |
| Cosine |
$cos~at$ |
$\dfrac{s}{s^2+a^2}$ |
| Hyperbolic sine |
$sinh~at$ |
$\dfrac{a}{s^2-a^2}$ |
| Hyperbolic cosine |
$cosh~at$ |
$\dfrac{s}{s^2-a^2}$ |
| Growing sine |
$t~sin~at$ |
$\dfrac{2as}{(s^2+a^2)^2}$ |
| Growing cosine |
$t~cos~at$ |
$\dfrac{s^2-a^2}{(s^2+a^2)^2}$ |
| Decaying sine |
$e^{-at}~sint$ |
$\dfrac{\omega }{\left ( s+a \right )^2+\omega ^2}$ |
| Decaying cosine |
$e^{-at}~cost$ |
$\dfrac{s+a }{\left ( s+a \right )^2+\omega ^2}$ |
| Delta function |
$\delta~(t)$ |
1 |
| Delayed delta |
$\delta(t-a)$ |
$e^{-{at}}$ |