(→Table of some Laplace transform) |
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| − | == Table of | + | == Table of Laplace transforms == |
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| + | We assume <math> s = j \omega </math> | ||
*<math> f(t) \rightarrow F(s) </math> | *<math> f(t) \rightarrow F(s) </math> | ||
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*<math> r(t) \rightarrow \frac{1}{s^2} </math> | *<math> r(t) \rightarrow \frac{1}{s^2} </math> | ||
*<math> t^{n} u(t) \rightarrow \frac{n!}{s^{n+1}} </math> | *<math> t^{n} u(t) \rightarrow \frac{n!}{s^{n+1}} </math> | ||
| + | *<math> e^{-at} \rightarrow \frac{1}{s+a} </math> | ||
| + | *<math> te^{-at} \rightarrow \frac{1}{(s+a)^{2}} </math> | ||
| + | *<math> t^{n}e^{-at} \rightarrow \frac{n!}{(s+a)^{n+1}} </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> 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> | ||
| + | *<math> tsin(\omega t)u(t) \rightarrow \frac{2\omega s}{(s^2+\omega ^2)^{2}} </math> | ||
| + | *<math> tcos(\omega t)u(t) \rightarrow \frac{(s^2 - \omega ^2)}{(s^2+\omega ^2)^{2}} </math> | ||
Latest revision as of 15:14, 24 November 2008
Table of Laplace transforms
We assume $ s = j \omega $
- $ 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}} $
- $ tsin(\omega t)u(t) \rightarrow \frac{2\omega s}{(s^2+\omega ^2)^{2}} $
- $ tcos(\omega t)u(t) \rightarrow \frac{(s^2 - \omega ^2)}{(s^2+\omega ^2)^{2}} $
