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Beliebt Rechnen >

inverselaplace 1/(s^2(s+1))

Lösung

inverse laplace transformation

\frac{1}{s ^{2} ( s + 1 )}

Lösung

- H (t) + t + e^{- t}

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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{1}{s + 1}}

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

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

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

= - H (t) + t + e^{- t}

Beliebte Beispiele

integral of (x^3-10x-3)

\int (x^{3} - 10 x - 3) d x

derivative a^3+cos^3(x)

d er i v a t i v e a^{3} + cos^{3} (x)

derivative of ln(1-2x)

\frac{d}{d x} (ln (1 - 2 x))

limit as x approaches infinity of 10

x \to \infty lim (10)

sum from n=1 to infinity of (n!)/(106^n)

n = 1 \sum \infty \frac{n !}{10 6 ^{n}}