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Beliebt Rechnen >

inverselaplace s/(4s^2+1)

Lösung

inverse laplace transformation

\frac{s}{4 s ^{2} + 1}

Lösung

\frac{1}{4} cos (\frac{t}{2})

Schritte zur Lösung

L^{- 1} {\frac{s}{4 s ^{2} + 1}}

Wende inverse Transformationsregel an: if

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

dann

L^{- 1} {s F (s)} = \frac{d}{d t} f (t) + f (0)

Für

\frac{s}{4 s ^{2} + 1} : F (s) = \frac{1}{4 s ^{2} + 1}

= \frac{d}{d t} (L^{- 1} {\frac{1}{4 s ^{2} + 1}}) + L^{- 1} {\frac{1}{4 s ^{2} + 1}} (0)

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

\frac{d}{d t} (\frac{1}{2} sin (\frac{t}{2})) = \frac{1}{4} cos (\frac{t}{2})

Evaluiere

\frac{1}{2} sin (\frac{t}{2})

am Punkt

0 = 0

= \frac{1}{4} cos (\frac{t}{2})

Beliebte Beispiele

derivative 6e^r

d er i v a t i v e 6 e^{r}

integral from 1 to 2 of (ln(x^7))/x

\int_{1}^{2} \frac{ln ( x ^{7} )}{x} d x

derivative-4.9t^2+25t+3

d er i v a t i v e - 4.9 t^{2} + 25 t + 3

integral from-2 to 2 of sqrt(2+|x|)

\int_{- 2}^{2} 2 + ∣ x ∣ d x

derivative x^2(580-x/3)

d er i v a t i v e x^{2} (580 - \frac{x}{3})