តារាងបំលែងឡាប្លាស

លរ f(t) F(s) សំគាល់
${\displaystyle u(t)={\begin{cases}0\quad &(t<0)\\{\frac {1}{2}}\quad &(t=0)\\1\quad &(t>0)\end{cases}}}$ ${\displaystyle {\frac {1}{s}}}$ អនុគមន៍កាំជណ្តើរហេវីសាយ
${\displaystyle \delta (t)={\begin{cases}\infty \quad &(t=0)\\0\quad &(t\neq 0)\end{cases}}}$ ${\displaystyle \,1}$ អនុគមន៍ដែលតា
${\displaystyle \alpha \,}$ ${\displaystyle {\frac {\alpha }{s}}}$
${\displaystyle {\frac {d^{n}}{dt^{n}}}\delta (t)\,}$ ${\displaystyle s^{n}\,}$ ${\displaystyle \delta (t)\,}$: អនុគមន៍ដែលតា
${\displaystyle e^{-{\alpha }t}\,}$ ${\displaystyle {\frac {1}{s+\alpha }}\,}$ អនុគមន៍អិចស្ប៉ូណង់ស្យែល
${\displaystyle \,\delta (t)-{\alpha }e^{-{\alpha }t}}$ ${\displaystyle {\frac {s}{s+\alpha }}\,}$ ${\displaystyle \delta (t)\,}$: អនុគមន៍ដែលតា
${\displaystyle {\frac {t^{n}}{n!}}\,}$ ${\displaystyle {\frac {1}{s^{n+1}}}\,}$ ${\displaystyle n\,}$: ចំនួនគត់ធម្មជាតិ
${\displaystyle {\frac {e^{-{\alpha }t}-e^{-{\beta }t}}{\beta -\alpha }}\,}$ ${\displaystyle {\frac {1}{(s+\alpha )(s+\beta )}}\,}$
${\displaystyle {\frac {(a-\alpha )e^{-{\alpha }t}-(a-\beta )e^{-{\beta }t}}{\beta -\alpha }}\,}$ ${\displaystyle {\frac {s+a}{(s+\alpha )(s+\beta )}}\,}$
១០ ${\displaystyle {\frac {1}{\alpha }}\sin {\alpha }t\,}$ ${\displaystyle {\frac {1}{s^{2}+{\alpha }^{2}}}\,}$
១១ ${\displaystyle {\frac {1}{\alpha }}\sinh {\alpha }t\,}$ ${\displaystyle {\frac {1}{s^{2}-{\alpha }^{2}}}\,}$
១២ ${\displaystyle \cos {\alpha }t\,}$ ${\displaystyle {\frac {s}{s^{2}+{\alpha }^{2}}}\,}$
១៣ ${\displaystyle \cosh {\alpha }t\,}$ ${\displaystyle {\frac {s}{s^{2}-{\alpha }^{2}}}\,}$
១៤ ${\displaystyle te^{-{\alpha }t}\,}$ ${\displaystyle {\frac {1}{(s+\alpha )^{2}}}\,}$
១៥ ${\displaystyle [(a-\alpha )t+1]e^{{-\alpha }t}\,}$ ${\displaystyle {\frac {s+a}{(s+\alpha )^{2}}}\,}$
១៦ ${\displaystyle {\frac {1}{\beta }}e^{-{\alpha }t}\sin {\beta }t\,}$ ${\displaystyle {\frac {1}{(s+\alpha )^{2}+{\beta }^{2}}}\,}$
១៧ ${\displaystyle e^{-{\alpha }t}\sin {\beta }t\,}$ ${\displaystyle {\frac {\beta }{(s+\alpha )^{2}+{\beta }^{2}}}\,}$ ${\displaystyle {\beta }^{2}>0\,}$
១៨ ${\displaystyle e^{-{\alpha }t}\cos {\beta }t\,}$ ${\displaystyle {\frac {s+\alpha }{(s+\alpha )^{2}+{\beta }^{2}}}\,}$ ${\displaystyle {\beta }^{2}>0\,}$
១៩ ${\displaystyle {\frac {1}{\beta }}[(a-\alpha )^{2}+{\beta }^{2}]^{\frac {1}{2}}e^{-{\alpha }t}\sin({\beta }t+\varphi )}$ ${\displaystyle {\frac {s+a}{(s+\alpha )^{2}+{\beta }^{2}}}\,}$ ${\displaystyle \varphi =\tan ^{-1}{\frac {\beta }{a-\alpha }}\,}$
២០ ${\displaystyle e^{-{\alpha }t}\sinh {\beta }t\,}$ ${\displaystyle {\frac {\beta }{(s+\alpha )^{2}-{\beta }^{2}}}\,}$
២១ ${\displaystyle e^{-{\alpha }t}\cosh {\beta }t\,}$ ${\displaystyle {\frac {s+\alpha }{(s+\alpha )^{2}-{\beta }^{2}}}\,}$
២២ ${\displaystyle {\frac {1}{{\alpha }{\beta }}}+{\frac {{\beta }e^{-{\alpha }t}-{\alpha }{e^{{-\beta }t}}}{{\alpha }{\beta }(\alpha -\beta )}}}$ ${\displaystyle {\frac {1}{s(s+\alpha )(s+\beta )}}\,}$
២៣ ${\displaystyle {\frac {a}{{\alpha }{\beta }}}+{\frac {a-\alpha }{{\alpha }(\alpha -\beta )}}e^{-{\alpha }t}+{\frac {a-\beta }{{\beta }(\alpha -\beta )}}e^{-{\beta }t}}$ ${\displaystyle {\frac {s+a}{s(s+\alpha )(s+\beta )}}\,}$
២៤ ${\displaystyle {\frac {e^{-{\alpha }t}}{(\beta -\alpha )(\gamma -\alpha )}}+{\frac {e^{-{\beta }t}}{(\alpha -\beta )(\gamma -\beta )}}+{\frac {e^{-{\gamma }t}}{(\alpha -\gamma )(\beta -\gamma )}}}$ ${\displaystyle {\frac {1}{(s+\alpha )(s+\beta )(s+\gamma )}}\,}$
២៥ ${\displaystyle {\frac {(a-\alpha )e^{-{\alpha }t}}{(\beta -\alpha )(\gamma -\alpha )}}+{\frac {(a-\beta )e^{-{\beta }t}}{(\alpha -\beta )(\gamma -\beta )}}+{\frac {(a-\gamma )e^{-{\gamma }t}}{(\alpha -\gamma )(\beta -\gamma )}}}$ ${\displaystyle {\frac {s+a}{(s+\alpha )(s+\beta )(s+\gamma )}}\,}$
២៦ ${\displaystyle {\frac {1}{{\alpha }^{2}}}(1-\cos {\alpha }t)\,}$ ${\displaystyle {\frac {1}{s(s^{2}+{\alpha }^{2})}}\,}$
២៧ ${\displaystyle {\frac {a}{{\alpha }^{2}}}-{\frac {(a^{2}+{\alpha }^{2})^{\frac {1}{2}}}{{\alpha }^{2}}}\cos({\alpha }t+\varphi )}$ ${\displaystyle {\frac {s+a}{s(s^{2}+{\alpha }^{2})}}\,}$ ${\displaystyle \varphi =\tan ^{-1}{\frac {\alpha }{a}}\,}$
២៨ ${\displaystyle {\frac {t}{\alpha }}-{\frac {1}{{\alpha }^{2}}}(1-e^{-{\alpha }t})}$ ${\displaystyle {\frac {1}{s^{2}(s+\alpha )}}\,}$
២៩ ${\displaystyle {\frac {a-\alpha }{{\alpha }^{2}}}e^{-{\alpha }t}+{\frac {a}{\alpha }}t-{\frac {\alpha -a}{{\alpha }^{2}}}}$ ${\displaystyle {\frac {s+a}{s^{2}(s+\alpha )}}\,}$
៣០ ${\displaystyle {\frac {1-(1+{\alpha }t)e^{-{\alpha }t}}{{\alpha }^{2}}}\,}$ ${\displaystyle {\frac {1}{s(s+\alpha )^{2}}}\,}$
៣១ ${\displaystyle {\frac {a}{{\alpha }^{2}}}\{1-[1+(1-{\frac {\alpha }{a}}){\alpha }t]e^{-{\alpha }t}\}}$ ${\displaystyle {\frac {s+a}{s(s+\alpha )^{2}}}\,}$
៣២
• ${\displaystyle \,{\omega }^{2}>{\alpha }^{2}}$
${\displaystyle {\frac {1}{{\omega }^{2}}}[1-{\frac {{\omega }_{0}}{\omega }}e^{-{\alpha }t}\sin({\omega }t+\varphi )]}$
• ${\displaystyle \,{\omega }^{2}={\alpha }^{2}}$
${\displaystyle {\frac {1}{{\omega }^{2}}}[1-e^{-{\alpha }t}(1+{\alpha }t)]}$
• ${\displaystyle \,{\omega }^{2}<{\alpha }^{2}}$
${\displaystyle {\frac {1}{{\omega }^{2}}}[1-{\frac {{\omega }_{0}^{2}}{n-m}}({\frac {e^{-mt}}{m}}-{\frac {e^{-nt}}{n}})]}$
${\displaystyle {\frac {1}{s(s+2{\alpha }s+{\omega }_{0}^{2})}}\,}$ {\displaystyle {\begin{aligned}\varphi &=\tan ^{-1}{\frac {\omega }{\alpha }}\\{\omega }^{2}&={\omega }_{0}^{2}-{\alpha }^{2}\end{aligned}}}

${\displaystyle \,m}$ និង ${\displaystyle \,n}$ ជារឹសនៃសមីការ
${\displaystyle \,s^{2}+2{\alpha }s+{\omega }_{0}^{2}=0}$