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Beliebt Rechnen >

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

Lösung

inverse laplace transformation

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

Lösung

\frac{1}{4} H (t) - \frac{1}{4} cos (2 t) + δ (t)

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

Wende die lineare Eigenschaftder inversen Laplace-Transformation an:

Für Funktionen

f (s), g (s)

und Konstanten

a, b : L^{- 1} {a \cdot f (s) + b \cdot g (s)} = a \cdot L^{- 1} {f (s)} + b \cdot L^{- 1} {g (s)}

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

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

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

L^{- 1} {1} : δ (t)

= \frac{1}{4} H (t) - \frac{1}{4} cos (2 t) + δ (t)

Beliebte Beispiele

limit as x approaches 0 of (4/(x-1)+4)/x

x \to 0 lim (\frac{\frac{4}{x - 1} + 4}{x})

derivative of sqrt(x/(x+2))

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

derivative e^{4xsin(2x)}

d er i v a t i v e e^{4 x s i n (2 x)}

derivative f(x)=x^3+5x

d er i v a t i v e f (x) = x^{3} + 5 x

(\partial)/(\partial x)(4e^{4xy})

\frac{\partial}{\partial x} (4 e^{4 x y})