laplacetransform 2cos(t)-2

Lösung

laplace transformation

2 cos (t) - 2

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

Schritte zur Lösung

L {2 cos (t) - 2}

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)}

= 2 L {cos (t)} - L {2}

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

L {2} : \frac{2}{s}

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

Vereinfache

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

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

\frac{d}{d x} (\frac{( 6 x ^{2} + 8 x + 8 )}{x})

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