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Beliebt Rechnen >

inverselaplace s/((s^2+4))

Lösung

inverse laplace transformation

\frac{s}{( s ^{2} + 4 )}

Lösung

cos (2 t)

Schritte zur Lösung

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

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

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

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

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

Evaluiere

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

am Punkt

0 = 0

= cos (2 t)

Beliebte Beispiele

limit as x approaches 1 of (x^2-2)^3

x \to 1 lim ((x^{2} - 2)^{3})

derivative f(x)=6sec(x)tan(x)

d er i v a t i v e f (x) = 6 sec (x) tan (x)

integral from 0 to 7 of 1/(sqrt(49+x^2))

\int_{0}^{7} \frac{1}{49 + x ^{2}} d x

integral of 1/(sqrt(4-y^2))

\int \frac{1}{4 - y ^{2}} d y

y^{^{'}} = sin (y)