តារាងបំលែងឡាប្លាស

លរ	f(t)	F(s)	សំគាល់
១	$u(t) = \begin{cases} 0 \quad &(t < 0) \\ \frac{1}{2} \quad &(t = 0) \\ 1 \quad &(t > 0) \end{cases}$	$\frac{1}{s}$	អនុគមន៍កាំជណ្តើរហេវីសាយ
២	$\delta (t)= \begin{cases} \infty \quad &(t=0)\\ 0 \quad &(t\neq 0) \end{cases}$	$\, 1$	អនុគមន៍ដែលតា
៣	$\alpha \,$	$\frac{\alpha}{s}$
៤	$\frac{d^n}{dt^n} \delta(t) \,$	$s^n \,$	$\delta (t)\,$: 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	$te^{-{\alpha}t} \,$	$\frac{1}{(s+\alpha)^2} \,$
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	$\frac{1}{\beta}[(a-\alpha)^2 + {\beta}^2]^{\frac{1}{2}}e^{-{\alpha}t}\sin ({\beta}t+\varphi)$	$\frac{s+a}{(s+\alpha)^2+{\beta}^2} \,$	$\varphi =\tan^{-1}\frac{\beta}{a-\alpha} \,$
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	$\frac{a}{{\alpha}^2} - \frac{(a^2 + {\alpha}^2)^{\frac{1}{2}}}{{\alpha}^2} \cos ({\alpha}t + \varphi)$	$\frac{s+a}{s(s^2+{\alpha}^2)} \,$	$\varphi = \tan^{-1}\frac{\alpha}{a} \,$
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	$\, {\omega}^2 > {\alpha}^2$ $\frac{1}{{\omega}^2}[1 - \frac{{\omega}_0}{\omega}e^{-{\alpha}t}\sin ({\omega}t + \varphi)]$ $\, {\omega}^2 = {\alpha}^2$ $\frac{1}{{\omega}^2}[1-e^{-{\alpha}t}(1+{\alpha}t)]$ $\,{\omega}^2 < {\alpha}^2$ $\frac{1}{{\omega}^2}[1 - \frac{{\omega}^2_0}{n-m}(\frac{e^{-mt}}{m} - \frac{e^{-nt}}{n})]$	$\frac{1}{s(s+2{\alpha}s+{\omega}^2_0)} \,$	$\begin{align}\varphi &= \tan^{-1}\frac{\omega}{\alpha}\\ {\omega}^2 &= {\omega}^2_0-{\alpha}^2 \end{align}$ $\, m$ និង $\, n$ ជារឹសនៃសមីការ $\, s^2+2{\alpha}s+{\omega}^2_0 = 0$

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