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	$\,{\omega }^{2}>{\alpha }^{2}$ ${\frac {1}{{\omega }^{2}}}[1-{\frac {{\omega }_{0}}{\omega }}e^{-{\alpha }t}\sin({\omega }t+\varphi )]$ $\,{\omega }^{2}={\alpha }^{2}$ ${\frac {1}{{\omega }^{2}}}[1-e^{-{\alpha }t}(1+{\alpha }t)]$ $\,{\omega }^{2}<{\alpha }^{2}$ ${\frac {1}{{\omega }^{2}}}[1-{\frac {{\omega }_{0}^{2}}{n-m}}({\frac {e^{-mt}}{m}}-{\frac {e^{-nt}}{n}})]$	${\frac {1}{s(s+2{\alpha }s+{\omega }_{0}^{2})}}\,$	${\begin{aligned}\varphi &=\tan ^{-1}{\frac {\omega }{\alpha }}\\{\omega }^{2}&={\omega }_{0}^{2}-{\alpha }^{2}\end{aligned}}$ $\,m$ និង $\,n$ ជារឹសនៃសមីការ $\,s^{2}+2{\alpha }s+{\omega }_{0}^{2}=0$

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