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Beliebt Rechnen >

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

Lösung

inverse laplace transformation

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

Lösung

- \frac{5}{4} H (t) + \frac{5 t}{2} + \frac{5}{4} e^{- 2 t}

Schritte zur Lösung

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

Ermittle den Partialbruch von

\frac{5}{s ^{2} ( s + 2 )} : - \frac{5}{4 s} + \frac{5}{2 s ^{2}} + \frac{5}{4 ( s + 2 )}

= L^{- 1} {- \frac{5}{4 s} + \frac{5}{2 s ^{2}} + \frac{5}{4 ( s + 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{5}{4 s}} + L^{- 1} {\frac{5}{2 s ^{2}}} + L^{- 1} {\frac{5}{4 ( s + 2 )}}

L^{- 1} {\frac{5}{4 s}} : \frac{5}{4} H (t)

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

L^{- 1} {\frac{5}{4 ( s + 2 )}} : \frac{5}{4} e^{- 2 t}

= - \frac{5}{4} H (t) + \frac{5 t}{2} + \frac{5}{4} e^{- 2 t}

Beliebte Beispiele

integral from 0 to 1 of xcos((npix)/2)

\int_{0}^{1} x cos (\frac{nπ x}{2}) d x

inverselaplace 1/((5*s+1))

in v erse l a pl a ce \frac{1}{( 5 \cdot s + 1 )}

integral of (x^4+2sqrt(x)-16)

\int (x^{4} + 2 x - 16) d x

derivative of a(1-cos(x))

\frac{d}{d x} (a (1 - cos (x)))

(\partial)/(\partial x)(e^{2y^2}+4x^2)

\frac{\partial}{\partial x} (e^{2 y^{2}} + 4 x^{2})