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Beliebt Rechnen >

inverselaplace (e^{-6s})/(s^2+2s-8)

Lösung

inverse laplace transformation

\frac{e ^{- 6 s}}{s ^{2} + 2 s - 8}

Lösung

H (t - 6) (\frac{1}{6} e^{2 (t - 6)} - \frac{1}{6} e^{- 4 (t - 6)})

Schritte zur Lösung

L^{- 1} {\frac{e ^{- 6 s}}{s ^{2} + 2 s - 8}}

Wende inverse Transformationsregel an: if

L^{- 1} {F (s)} = f (t)

dann

L^{- 1} {e^{- a s} F (s)} = H (t - a) f (t - a)

Wo

H (t)

Heaviside (Schritt) Funktion ist

= H (t - 6) L^{- 1} {\frac{1}{s ^{2} + 2 s - 8}} (t - 6)

L^{- 1} {\frac{1}{s ^{2} + 2 s - 8}} : \frac{1}{6} e^{2 t} - \frac{1}{6} e^{- 4 t}

= H (t - 6) (\frac{1}{6} e^{2 (t - 6)} - \frac{1}{6} e^{- 4 (t - 6)})

Beliebte Beispiele

integral of (4x+x^2)/(x^2)

\int \frac{4 x + x ^{2}}{x ^{2}} d x

(\partial)/(\partial x)(xyz-z-sin(x+y))

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

derivative f(x)=ln((x-2)/(x+1))

d er i v a t i v e f (x) = ln (\frac{x - 2}{x + 1})

integral of x(7-y)

\int x (7 - y)

integral of 1/(9-4x^2)

\int \frac{1}{9 - 4 x ^{2}} d x