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Beliebt Rechnen >

laplacetransform f(t)=3sin(4t)-2e^{2t}

Lösung

laplace transformation

f (t) = 3 sin (4 t) - 2 e^{2 t}

Lösung

\frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

Schritte zur Lösung

L {3 sin (4 t) - 2 e^{2 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)}

= 3 L {sin (4 t)} - 2 L {e^{2 t}}

L {sin (4 t)} : \frac{4}{s ^{2} + 16}

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

= 3 \cdot \frac{4}{s ^{2} + 16} - 2 \cdot \frac{1}{s - 2}

Fasse

3 \frac{4}{s ^{2} + 16} - 2 \frac{1}{s - 2}

zusammen:

\frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

= \frac{12}{s ^{2} + 16} - \frac{2}{s - 2}

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