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Beliebt Rechnen >

laplacetransform 3sin(sqrt(2)t)-3cos(sqrt(2)t)

Lösung

laplace transformation

3 sin (2 t) - 3 cos (2 t)

Lösung

\frac{3 2}{s ^{2} + 2} - \frac{3 s}{s ^{2} + 2}

Schritte zur Lösung

L {3 sin (2 t) - 3 cos (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 (2 t)} - 3 L {cos (2 t)}

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

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

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

Fasse

3 \frac{2}{s ^{2} + 2} - 3 \frac{s}{s ^{2} + 2}

zusammen:

\frac{3 2}{s ^{2} + 2} - \frac{3 s}{s ^{2} + 2}

= \frac{3 2}{s ^{2} + 2} - \frac{3 s}{s ^{2} + 2}

Beliebte Beispiele

derivative of x^y-y^x

\frac{d}{d x} (x^{y} - y^{x})

y^{^{'}} - y = x^{2}

limit as x approaches 7 of sqrt(3x-5)

x \to 7 lim (3 x - 5)

limit as x approaches 0 of (2x^2+5x+7)/x

x \to 0 lim (\frac{2 x ^{2} + 5 x + 7}{x})

derivative of cos(sin(5x))

\frac{d}{d x} (cos (sin (5 x)))