Inverse Laplace Transform Table

Electrical Workbook — Wed, 05 Jun 2019 23:08:21 +0000

In this topic, you study the Table of Inverse Laplace Transforms.

Definition: If Laplace transform $L[f(t)]=F(s)$ then inverse Laplace transform ${L^{ – 1}}[F(s)] = f(t)$. Using above property, the inverse Laplace transform of standard forms are

\[{L^{ – 1}}[F(s)]\]	\[f(t)\]
\[{L^{ – 1}}\left[ {\frac{1}{s}} \right]\]	\[u(t)\]
\[{L^{ – 1}}\left[ {\frac{1}{{{s^2}}}} \right]\]	\[t \]
\[{L^{ – 1}}\left[ {\frac{{n!}}{{{s^{n + 1}}}}} \right]\]	\[{t^n} \]
\[{L^{ – 1}}\left[ {\frac{1}{{s + a}}} \right]\]	\[{e^{ – at}}\]
\[{L^{ – 1}}\left[ {\frac{1}{{s – a}}} \right]\]	\[{e^{ at}}\]
\[{L^{ – 1}}\left[ {\frac{a}{{{s^2} + {a^2}}}} \right]\]	\[\sin at\]
\[{L^{ – 1}}\left[ {\frac{s}{{{s^2} + {a^2}}}} \right]\]	\[\cos at\]
\[{L^{ – 1}}\left[ {\frac{a}{{{s^2} – {a^2}}}} \right]\]	\[\sinh at\]
\[{L^{ – 1}}\left[ {\frac{s}{{{s^2} – {a^2}}}} \right]\]	\[\cosh at\]

Note:- Defined for $t$ ≥ 0, $f(t)$ = 0, for $t$ < 0.

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Laplace Transform Table

Electrical Workbook — Wed, 05 Jun 2019 22:31:12 +0000

In this topic, you study the Table of Laplace Transforms.

Definition: Laplace transform of $f(t)$ is

\[L[f(t)] = F(s) = \int\limits_0^\infty {f(t){e^{ – st}}dt}\]

Using above property, the Laplace transform of Basic Functions are

\[L[f(t)] \]	\[F(s)\]
\[L[u(t)] \]	\[ \frac{1}{s} \]
\[L[t] \]	\[ \frac{1}{{{s^2}}} \]
\[L[{t^n}] \]	\[ \frac{{n!}}{{{s^{n + 1}}}} \]
\[L[{e^{ – at}}] \]	\[\frac{1}{{s+a}} \]
\[L[e^{ at}] \]	\[\frac{1}{{s-a}} \]
\[L[\sin at] \]	\[ \frac{{a}}{{{s^2} + a^2}} \]
\[L[\cos at] \]	\[ \frac{{s}}{{{s^2} + a^2}} \]
\[L[\sinh at] \]	\[ \frac{{a}}{{{s^2} – a^2}} \]
\[L[\cosh at] \]	\[ \frac{{s}}{{{s^2} – a^2}} \]

Note:- Defined for $t$ ≥ 0, $f(t)$ = 0, for $t$ < 0.

The post Laplace Transform Table appeared first on ElectricalWorkbook.

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Inverse Laplace Transform Table

Laplace Transform Table