inverselaplace 4/((s-4)^3)

Lösung

inverse laplace transformation

\frac{4}{( s - 4 ) ^{3}}

e^{4 t} \cdot 2 t^{2}

Schritte zur Lösung

L^{- 1} {\frac{4}{( s - 4 ) ^{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{4}{( s - 4 ) ^{3}} : a = 4, F (s) = \frac{4}{s ^{3}}

= e^{4 t} L^{- 1} {\frac{4}{s ^{3}}}

L^{- 1} {\frac{4}{s ^{3}}} : 2 t^{2}

= e^{4 t} \cdot 2 t^{2}

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