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Beliebt Rechnen >

laplacetransform (t-5)^2

Lösung

laplace transformation

(t - 5)^{2}

Lösung

\frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

Schritte zur Lösung

L {(t - 5)^{2}}

Schreibe

(t - 5)^{2}

um:

t^{2} - 10 t + 25

= L {t^{2} - 10 t + 25}

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}} - 10 L {t} + L {25}

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

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

L {25} : \frac{25}{s}

= \frac{2}{s ^{3}} - 10 \cdot \frac{1}{s ^{2}} + \frac{25}{s}

Fasse

\frac{2}{s ^{3}} - 10 \frac{1}{s ^{2}} + \frac{25}{s}

zusammen:

\frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

= \frac{2}{s ^{3}} - \frac{10}{s ^{2}} + \frac{25}{s}

Beliebte Beispiele

\int - π d x

sum from n=-4 to infinity of (-4/7)^n

n = - 4 \sum \infty (- \frac{4}{7})^{n}

integral of 1/((1-2x)^4sqrt(4x^2-4x-4))

\int \frac{1}{( 1 - 2 x ) ^{4} 4 x ^{2} - 4 x - 4} d x

derivative of 3/(1+3x)

\frac{d}{d x} (\frac{3}{1 + 3 x})

integral of 4/65 x^3

\int \frac{4}{65} x^{3} d x