តារាងបំលែងឡាប្លាស

លរ	f(t)	F(s)	សំគាល់
១	$u(t)=\{\begin{array}{cc}0& (t<0)\\ \frac{1}{2}& (t=0)\\ 1& (t>0)\end{array}$	$\frac{1}{s}$	អនុគមន៍កាំជណ្តើរហេវីសាយ
២	$\delta (t)=\{\begin{array}{cc}\mathrm{\infty }& (t=0)\\ 0& (t\ne 0)\end{array}$	$1$	អនុគមន៍ដែលតា
៣	$\alpha$	$\frac{\alpha }{s}$
៤	$\frac{d^n}{d{t}^n}\delta (t)$	$s^n$	$\delta (t)$: អនុគមន៍ដែលតា
៥	$e^{-\alpha t}$	$\frac{1}{s+\alpha }$	អនុគមន៍អិចស្ប៉ូណង់ស្យែល
៦	$\delta (t)-\alpha e^{-\alpha t}$	$\frac{s}{s+\alpha }$	$\delta (t)$: អនុគមន៍ដែលតា
៧	$\frac{t^n}{n!}$	$\frac{1}{s^{n+1}}$	$n$: ចំនួនគត់ធម្មជាតិ
៨	$\frac{e^{-\alpha t}-e^{-\beta t}}{\beta -\alpha }$	$\frac{1}{(s+\alpha )(s+\beta )}$
៩	$\frac{(a-\alpha )e^{-\alpha t}-(a-\beta )e^{-\beta t}}{\beta -\alpha }$	$\frac{s+a}{(s+\alpha )(s+\beta )}$
១០	$\frac{1}{\alpha }\sin \alpha t$	$\frac{1}{s^2+{\alpha }^2}$
១១	$\frac{1}{\alpha }\sinh \alpha t$	$\frac{1}{s^2-{\alpha }^2}$
១២	$\cos \alpha t$	$\frac{s}{s^2+{\alpha }^2}$
១៣	$\cosh \alpha t$	$\frac{s}{s^2-{\alpha }^2}$
១៤	$t{e}^{-\alpha t}$	$\frac{1}{(s+\alpha {)}^2}$
១៥	$[(a-\alpha )t+1]e^{-\alpha t}$	$\frac{s+a}{(s+\alpha {)}^2}$
១៦	$\frac{1}{\beta }{e}^{-\alpha t}\sin \beta t$	$\frac{1}{(s+\alpha {)}^2+{\beta }^2}$
១៧	$e^{-\alpha t}\sin \beta t$	$\frac{\beta }{(s+\alpha {)}^2+{\beta }^2}$	${\beta }^2>0$
១៨	$e^{-\alpha t}\cos \beta t$	$\frac{s+\alpha }{(s+\alpha {)}^2+{\beta }^2}$	${\beta }^2>0$
១៩	$\frac{1}{\beta }[(a-\alpha {)}^2+{\beta }^2{]}^{\frac{1}{2}}{e}^{-\alpha t}\sin (\beta t+\phi )$	$\frac{s+a}{(s+\alpha {)}^2+{\beta }^2}$	$\phi ={\tan }^{-1}\frac{\beta }{a-\alpha }$
២០	$e^{-\alpha t}\sinh \beta t$	$\frac{\beta }{(s+\alpha {)}^2-{\beta }^2}$
២១	$e^{-\alpha t}\cosh \beta t$	$\frac{s+\alpha }{(s+\alpha {)}^2-{\beta }^2}$
២២	$\frac{1}{\alpha \beta }+\frac{\beta e^{-\alpha t}-\alpha e^{-\beta t}}{\alpha \beta (\alpha -\beta )}$	$\frac{1}{s(s+\alpha )(s+\beta )}$
២៣	$\frac{a}{\alpha \beta }+\frac{a-\alpha }{\alpha (\alpha -\beta )}{e}^{-\alpha t}+\frac{a-\beta }{\beta (\alpha -\beta )}{e}^{-\beta t}$	$\frac{s+a}{s(s+\alpha )(s+\beta )}$
២៤	$\frac{e^{-\alpha t}}{(\beta -\alpha )(\gamma -\alpha )}+\frac{e^{-\beta t}}{(\alpha -\beta )(\gamma -\beta )}+\frac{e^{-\gamma t}}{(\alpha -\gamma )(\beta -\gamma )}$	$\frac{1}{(s+\alpha )(s+\beta )(s+\gamma )}$
២៥	$\frac{(a-\alpha )e^{-\alpha t}}{(\beta -\alpha )(\gamma -\alpha )}+\frac{(a-\beta )e^{-\beta t}}{(\alpha -\beta )(\gamma -\beta )}+\frac{(a-\gamma )e^{-\gamma t}}{(\alpha -\gamma )(\beta -\gamma )}$	$\frac{s+a}{(s+\alpha )(s+\beta )(s+\gamma )}$
២៦	$\frac{1}{{\alpha }^2}(1-\cos \alpha t)$	$\frac{1}{s(s^2+{\alpha }^2)}$
២៧	$\frac{a}{{\alpha }^2}-\frac{(a^2+{\alpha }^2{)}^{\frac{1}{2}}}{{\alpha }^2}\cos (\alpha t+\phi )$	$\frac{s+a}{s(s^2+{\alpha }^2)}$	$\phi ={\tan }^{-1}\frac{\alpha }{a}$
២៨	$\frac{t}{\alpha }-\frac{1}{{\alpha }^2}(1-e^{-\alpha t})$	$\frac{1}{s^2(s+\alpha )}$
២៩	$\frac{a-\alpha }{{\alpha }^2}{e}^{-\alpha t}+\frac{a}{\alpha }t-\frac{\alpha -a}{{\alpha }^2}$	$\frac{s+a}{s^2(s+\alpha )}$
៣០	$\frac{1-(1+\alpha t)e^{-\alpha t}}{{\alpha }^2}$	$\frac{1}{s(s+\alpha {)}^2}$
៣១	$\frac{a}{{\alpha }^2}\{1-[1+(1-\frac{\alpha }{a})\alpha t]e^{-\alpha t}\}$	$\frac{s+a}{s(s+\alpha {)}^2}$
៣២	${\omega }^2>{\alpha }^2$ $\frac{1}{{\omega }^2}[1-\frac{{\omega }_0}{\omega }{e}^{-\alpha t}\sin (\omega t+\phi )]$ ${\omega }^2={\alpha }^2$ $\frac{1}{{\omega }^2}[1-e^{-\alpha t}(1+\alpha t)]$ ${\omega }^2<{\alpha }^2$ $\frac{1}{{\omega }^2}[1-\frac{{\omega }_0^2}{n-m}(\frac{e^{-mt}}{m}-\frac{e^{-nt}}{n})]$	$\frac{1}{s(s+2\alpha s+{\omega }_0^2)}$	$\begin{array}{cc}\phi & ={\tan }^{-1}\frac{\omega }{\alpha }\\ {\omega }^2& ={\omega }_0^2-{\alpha }^2\end{array}$ $m$ និង $n$ ជារឹសនៃសមីការ $s^2+2\alpha s+{\omega }_0^2=0$

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