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Beliebt Rechnen >

laplacetransform {t^2-3t-2e^{-t}sin(3t)}

Lösung

laplace transformation

{t^{2} - 3 t - 2 e^{- t} sin (3 t)}

Lösung

\frac{2}{s ^{3}} - \frac{3}{s ^{2}} - \frac{6}{( s + 1 ) ^{2} + 9}

Schritte zur Lösung

L {t^{2} - 3 t - 2 e^{- t} sin (3 t)}

Verwende die lineare Eigenschaft der Laplace-Transformation:

Für Funktionen

f (t), g (t)

und Konstanten

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {t^{2}} - 3 L {t} - 2 L {e^{- t} sin (3 t)}

L {t^{2}} : \frac{2}{s ^{3}}

L {t} : \frac{1}{s ^{2}}

L {e^{- t} sin (3 t)} : \frac{3}{( s + 1 ) ^{2} + 9}

= \frac{2}{s ^{3}} - 3 \cdot \frac{1}{s ^{2}} - 2 \cdot \frac{3}{( s + 1 ) ^{2} + 9}

Fasse

\frac{2}{s ^{3}} - 3 \frac{1}{s ^{2}} - 2 \frac{3}{( s + 1 ) ^{2} + 9}

zusammen:

\frac{2}{s ^{3}} - \frac{3}{s ^{2}} - \frac{6}{( s + 1 ) ^{2} + 9}

= \frac{2}{s ^{3}} - \frac{3}{s ^{2}} - \frac{6}{( s + 1 ) ^{2} + 9}

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