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Beliebt Rechnen >

laplacetransform t^3e^{-0.1t}

Lösung

laplace transformation

t^{3} e^{- 0.1 t}

Lösung

\frac{6}{( s + 0.1 ) ^{4}}

Schritte zur Lösung

L {e^{- 0.1 t} t^{3}}

Wende Laplace-Transformationstabelle an:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

Für

t^{3} e^{- 0.1 t} : f (t) = e^{- 0.1 t}, k = 3

= (- 1)^{3} \frac{d ^{3}}{d s ^{3}} (L {e^{- 0.1 t}})

L {e^{- 0.1 t}} : \frac{1}{s + 0.1}

\frac{d ^{3}}{d s ^{3}} (\frac{1}{s + 0.1}) = - \frac{6}{( s + 0.1 ) ^{4}}

= (- 1)^{3} (- \frac{6}{( s + 0.1 ) ^{4}})

= \frac{6}{( s + 0.1 ) ^{4}}

Beliebte Beispiele

integral from 1 to infinity of 1/(e^x)

\int_{1}^{\infty} \frac{1}{e ^{x}} d x

integral of sin(3x)sin(5x)

\int sin (3 x) sin (5 x) d x

integral of 8cos(t)

\int 8 cos (t) d t

(dy)/(dx)= y/(1+x)

\frac{d y}{d x} = \frac{y}{1 + x}

integral from 1 to 2 of 1/(x-1)

\int_{1}^{2} \frac{1}{x - 1} d x