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Beliebt Rechnen >

inverselaplace (se^{-3s})/((s-4)^3)

Lösung

inverse laplace transformation

\frac{s e ^{- 3 s}}{( s - 4 ) ^{3}}

Lösung

H (t - 3) (e^{4 (t - 3)} (t - 3) + e^{4 (t - 3)} \cdot 2 (t - 3)^{2})

Schritte zur Lösung

L^{- 1} {\frac{e ^{- 3 s} s}{( s - 4 ) ^{3}}}

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 - 3) L^{- 1} {\frac{s}{( s - 4 ) ^{3}}} (t - 3)

L^{- 1} {\frac{s}{( s - 4 ) ^{3}}} : e^{4 t} t + e^{4 t} \cdot 2 t^{2}

= H (t - 3) (e^{4 (t - 3)} (t - 3) + e^{4 (t - 3)} \cdot 2 (t - 3)^{2})

Beliebte Beispiele

derivative of sin(13x)

\frac{d}{d x} (sin (13 x))

(\partial)/(\partial h)(1/3 pir^2h)

\frac{\partial}{\partial h} (\frac{1}{3} π r^{2} h)

derivative of-x^2+x

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

derivative f(t)=t^2+4t

d er i v a t i v e f (t) = t^{2} + 4 t

integral of 1/((1+y)^2)

\int \frac{1}{( 1 + y ) ^{2}} d y