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Beliebt Rechnen >

inverselaplace 4/(s(s+2)^2)

Lösung

inverse laplace transformation

\frac{4}{s ( s + 2 ) ^{2}}

Lösung

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

Schritte zur Lösung

L^{- 1} {\frac{4}{s ( s + 2 ) ^{2}}}

Ermittle den Partialbruch von

\frac{4}{s ( s + 2 ) ^{2}} : \frac{1}{s} - \frac{1}{s + 2} - \frac{2}{( s + 2 ) ^{2}}

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

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

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

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

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

Beliebte Beispiele

derivative of log_{5}(tan(x))

\frac{d}{d x} (lo g_{5} (tan (x)))

limit as x approaches 4-of cx^2+3x

x \to 4 - lim (c x^{2} + 3 x)

integral of 2x^3-20x^{-5}

\int 2 x^{3} - 20 x^{- 5} d x

sum from n=0 to infinity of (2^n)/(8^n)

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

derivative of 4x+3/x

\frac{d}{d x} (4 x + \frac{3}{x})