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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

derivative of (1-x/(x^2+1))

\frac{d}{d x} (\frac{1 - x}{x ^{2} + 1})

y^{^{''}} - 4 y + 4 y = 0

y^{^{'}} = x (2 - y)

limit as x approaches-infinity of-3e^x

x \to - \infty lim (- 3 e^{x})

derivative of |x^4-4x^2|

\frac{d}{d x} (x^{4} - 4 x^{2})