laplacetransform 3(t-2)^2+13(t-2)+17

Lösung

laplace transformation

3 (t - 2)^{2} + 13 (t - 2) + 17

\frac{6}{s ^{3}} + \frac{1}{s ^{2}} + \frac{3}{s}

Schritte zur Lösung

L {3 (t - 2)^{2} + 13 (t - 2) + 17}

Schreibe

3 (t - 2)^{2} + 13 (t - 2) + 17

um:

3 t^{2} + t + 3

= L {3 t^{2} + t + 3}

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 {t^{2}} + L {t} + L {3}

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

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

L {3} : \frac{3}{s}

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

Fasse

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

zusammen:

\frac{6}{s ^{3}} + \frac{1}{s ^{2}} + \frac{3}{s}

= \frac{6}{s ^{3}} + \frac{1}{s ^{2}} + \frac{3}{s}

n = 0 \sum \infty n (1 - p)^{n - 1}

\int_{1}^{3} \frac{1}{x} d x

\int \frac{14 x ^{2} + 8 x - 5}{x ^{3} + x ^{2}} d x

\frac{d}{d t} (\frac{e ^{- t} - e ^{- t} t}{e ^{t}})

n = 0 \sum \infty n (\frac{2}{3})^{n}