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Beliebt Rechnen >

inverselaplace 1/(((s+1)^2+4))

Lösung

inverse laplace transformation

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

Lösung

e^{- t} \frac{1}{2} sin (2 t)

Schritte zur Lösung

L^{- 1} ⎩ ⎨ ⎧ \frac{1}{( ( s + 1 ) ^{2} + 4 )} ⎭ ⎬ ⎫

Wende inverse Transformationsregel an: if

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

dann

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

Für

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

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

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

= e^{- t} \frac{1}{2} sin (2 t)

Beliebte Beispiele

integral of sin^5(tco)s^4t

\int sin^{5} (t co) s^{4} t d t

derivative of ,xe^y

\frac{d}{d x} (, x e^{y})

tangent ln(x^2-24)=x-y+6

t an g e n t ln (x^{2} - 24) = x - y + 6

integral of 4cos^2(31x)

\int 4 cos^{2} (31 x) d x

integral from 1 to 2 of x-sqrt(x)

\int_{1}^{2} x - x d x