inverselaplace 3/((s-3)^3)

Lösung

inverse laplace transformation

\frac{3}{( s - 3 ) ^{3}}

\frac{3 e ^{3 t} t ^{2}}{2}

Schritte zur Lösung

L^{- 1} {\frac{3}{( s - 3 ) ^{3}}}

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {F (s - a)} = e^{a t} f (t)

Für

\frac{3}{( s - 3 ) ^{3}} : a = 3, F (s) = \frac{3}{s ^{3}}

= e^{3 t} L^{- 1} {\frac{3}{s ^{3}}}

L^{- 1} {\frac{3}{s ^{3}}} : \frac{3 t ^{2}}{2}

= \frac{3 e ^{3 t} t ^{2}}{2}

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