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Beliebt Rechnen >

inverselaplace 3/s+8/(s(s+1))

Lösung

inverse laplace transformation

\frac{3}{s} + \frac{8}{s ( s + 1 )}

Lösung

11 H (t) - 8 e^{- t}

Schritte zur Lösung

L^{- 1} {\frac{3}{s} + \frac{8}{s ( s + 1 )}}

Ermittle den Partialbruch von

\frac{8}{s ( s + 1 )} : \frac{8}{s} - \frac{8}{s + 1}

= L^{- 1} {\frac{3}{s} + \frac{8}{s} - \frac{8}{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{3}{s}} + L^{- 1} {\frac{8}{s}} - L^{- 1} {\frac{8}{s + 1}}

L^{- 1} {\frac{3}{s}} : 3 H (t)

L^{- 1} {\frac{8}{s}} : 8 H (t)

L^{- 1} {\frac{8}{s + 1}} : 8 e^{- t}

= 3 H (t) + 8 H (t) - 8 e^{- t}

Fasse

3 H (t) + 8 H (t) - 8 e^{- t}

zusammen:

11 H (t) - 8 e^{- t}

= 11 H (t) - 8 e^{- t}

Beliebte Beispiele

derivative of 7x+5

\frac{d}{d x} (7 x + 5)

integral of (1+sqrt(x))^{14}

\int (1 + x)^{14} d x

derivative of sqrt(sin(\sqrt{1+x^2)})

\frac{d}{d x} (sin (1 + x^{2}))

derivative of x^3+6x^2-15x

\frac{d}{d x} (x^{3} + 6 x^{2} - 15 x)

integral of 2e^{-2x}(x^2-2x+1)

\int 2 e^{- 2 x} (x^{2} - 2 x + 1) d x