inverselaplace (e^{(-pi)/2})/(s^2+9)

Lösung

inverse laplace transformation

\frac{e ^{\frac{- π}{2}}}{s ^{2} + 9}

\frac{1}{3 e ^{\frac{π}{2}}} sin (3 t)

Schritte zur Lösung

L^{- 1} {\frac{e ^{\frac{- π}{2}}}{s ^{2} + 9}}

= L^{- 1} {\frac{1}{3 e ^{\frac{π}{2}}} \cdot \frac{3}{s ^{2} + 3 ^{2}}}

Wende die konstante Multiplikationseigenschaft der inversen Laplace-Transformation an:

Für Funktionen

f (t)

und Konstante

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{1}{3 e ^{\frac{π}{2}}} L^{- 1} {\frac{3}{s ^{2} + 3 ^{2}}}

Verwende inverse Laplace-Transformationstabelle:

L^{- 1} {\frac{a}{s ^{2} + a ^{2}}} = sin (a t)

L^{- 1} {\frac{3}{s ^{2} + 3 ^{2}}} = sin (3 t)

= \frac{1}{3 e ^{\frac{π}{2}}} sin (3 t)

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