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Beliebt Rechnen >

inverselaplace (10)/(s*(s+5)^2)

Lösung

inverse laplace transformation

\frac{10}{s \cdot ( s + 5 ) ^{2}}

Lösung

\frac{2}{5} H (t) - \frac{2}{5} e^{- 5 t} - e^{- 5 t} \cdot 2 t

Schritte zur Lösung

L^{- 1} {\frac{10}{s ( s + 5 ) ^{2}}}

Ermittle den Partialbruch von

\frac{10}{s ( s + 5 ) ^{2}} : \frac{2}{5 s} - \frac{2}{5 ( s + 5 )} - \frac{2}{( s + 5 ) ^{2}}

= L^{- 1} {\frac{2}{5 s} - \frac{2}{5 ( s + 5 )} - \frac{2}{( s + 5 ) ^{2}}}

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

= L^{- 1} {\frac{2}{5 s}} - L^{- 1} {\frac{2}{5 ( s + 5 )}} - L^{- 1} {\frac{2}{( s + 5 ) ^{2}}}

L^{- 1} {\frac{2}{5 s}} : \frac{2}{5} H (t)

L^{- 1} {\frac{2}{5 ( s + 5 )}} : \frac{2}{5} e^{- 5 t}

L^{- 1} {\frac{2}{( s + 5 ) ^{2}}} : e^{- 5 t} \cdot 2 t

= \frac{2}{5} H (t) - \frac{2}{5} e^{- 5 t} - e^{- 5 t} \cdot 2 t

Beliebte Beispiele

integral from 0 to 4 of \sqrt[3]{2x}

\int_{0}^{4} 3 2 x d x

derivative (x^2-4x+3)/(x^2)

d er i v a t i v e \frac{x ^{2} - 4 x + 3}{x ^{2}}

7y^{''}+7y^'-14y=0

7 y^{^{''}} + 7 y^{^{'}} - 14 y = 0

derivative 7(3x^2ln(5x)+x^2)

d er i v a t i v e 7 (3 x^{2} ln (5 x) + x^{2})

limit as x approaches 2+of sqrt(8-x^3)

x \to 2 + lim (8 - x^{3})