(→Table of some Laplace transform) |
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*<math> sin(\omega t)u(t) \rightarrow \frac{\omega}{s^{2}+w^{2}} </math> | *<math> sin(\omega t)u(t) \rightarrow \frac{\omega}{s^{2}+w^{2}} </math> | ||
*<math> cos(\omega t)u(t) \rightarrow \frac{s}{s^{2}+w^{2}} </math> | *<math> cos(\omega t)u(t) \rightarrow \frac{s}{s^{2}+w^{2}} </math> | ||
| + | *<math> e^{-at}sin(\omega t)u(t) \rightarrow \frac{\omega}{(s+a)^{2}+w^{2}} </math> | ||
| + | *<math> e^{-at}cos(\omega t)u(t) \rightarrow \frac{s+a}{(s+a)^{2}+w^{2}} </math> | ||
Revision as of 15:12, 24 November 2008
Table of some Laplace transform
- $ f(t) \rightarrow F(s) $
- $ K \delta(t) \rightarrow K $
- $ K u(t) \rightarrow \frac{K}{s} $
- $ r(t) \rightarrow \frac{1}{s^2} $
- $ t^{n} u(t) \rightarrow \frac{n!}{s^{n+1}} $
- $ e^{-at} \rightarrow \frac{1}{s+a} $
- $ te^{-at} \rightarrow \frac{1}{(s+a)^{2}} $
- $ t^{n}e^{-at} \rightarrow \frac{n!}{(s+a)^{n+1}} $
- $ sin(\omega t)u(t) \rightarrow \frac{\omega}{s^{2}+w^{2}} $
- $ cos(\omega t)u(t) \rightarrow \frac{s}{s^{2}+w^{2}} $
- $ e^{-at}sin(\omega t)u(t) \rightarrow \frac{\omega}{(s+a)^{2}+w^{2}} $
- $ e^{-at}cos(\omega t)u(t) \rightarrow \frac{s+a}{(s+a)^{2}+w^{2}} $
