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Beliebt Rechnen >

laplacetransform (t-1)^2

Lösung

laplace transformation

(t - 1)^{2}

Lösung

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

Schritte zur Lösung

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

Schreibe

(t - 1)^{2}

um:

t^{2} - 2 t + 1

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

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

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

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

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

Fasse

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

zusammen:

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

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

Beliebte Beispiele

derivative of (x^3/2)

\frac{d}{d x} (\frac{x ^{3}}{2})

limit as x approaches 2+of 4x^2-2x+3

x \to 2 + lim (4 x^{2} - 2 x + 3)

tangent f(x)=7sqrt(x),\at x=25

t an g e n t f (x) = 7 x, at x = 25

derivative ln(x^{3/2})

d er i v a t i v e ln (x^{\frac{3}{2}})

inverselaplace (10)/(s(s+2))

in v erse l a pl a ce \frac{10}{s ( s + 2 )}