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Beliebt Rechnen >

laplacetransform (t^2-1)^2

Lösung

laplace transformation

(t^{2} - 1)^{2}

Lösung

\frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

Schritte zur Lösung

L {(t^{2} - 1)^{2}}

Schreibe

(t^{2} - 1)^{2}

um:

t^{4} - 2 t^{2} + 1

= L {t^{4} - 2 t^{2} + 1}

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^{4}} - 2 L {t^{2}} + L {1}

L {t^{4}} : \frac{24}{s ^{5}}

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

L {1} : \frac{1}{s}

= \frac{24}{s ^{5}} - 2 \cdot \frac{2}{s ^{3}} + \frac{1}{s}

Fasse

\frac{24}{s ^{5}} - 2 \frac{2}{s ^{3}} + \frac{1}{s}

zusammen:

\frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

= \frac{24}{s ^{5}} - \frac{4}{s ^{3}} + \frac{1}{s}

Beliebte Beispiele

derivative of x^{e^{x^2}}

\frac{d}{d x} (x^{e^{x^{2}}})

limit as x approaches-19+of sqrt(x+19)

x \to - 19 + lim (x + 19)

integral of e^{inx}

\int e^{in x} d x

integral of-ye^{-y}

\int - y e^{- y} d y

derivative of (sqrt(x)/(8+x))

\frac{d}{d x} (\frac{x}{8 + x})