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Beliebt Rechnen >

inverselaplace (e^{-pis})/(s^2+4)

Lösung

inverse laplace transformation

\frac{e ^{- π s}}{s ^{2} + 4}

Lösung

H (t - π) \frac{1}{2} sin (2 (t - π))

Schritte zur Lösung

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

Wende inverse Transformationsregel an: if

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

dann

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

Wo

H (t)

Heaviside (Schritt) Funktion ist

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

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

= H (t - π) \frac{1}{2} sin (2 (t - π))

Beliebte Beispiele

derivative of 40(x^2-2x)

\frac{d}{d x} (40 (x^{2} - 2 x))

derivative of pix^7-2x^5-5x^{-2}

\frac{d}{d x} (π x^{7} - 2 x^{5} - 5 x^{- 2})

derivative (x^2-4)/(sqrt(x))

d er i v a t i v e \frac{x ^{2} - 4}{x}

derivative 8sin(x)

d er i v a t i v e 8 sin (x)

f (x) = x^{\frac{3}{5}}