laplacetransform (t-6.8)sin(6.2t)

Lösung

laplace transformation

(t - 6.8) sin (6.2 t)

\frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}} - \frac{42.16}{s ^{2} + 38.44}

Schritte zur Lösung

L {sin (6.2 t) (t - 6.8)}

Schreibe

(t - 6.8) sin (6.2 t)

um:

t sin (6.2 t) - 6.8 sin (6.2 t)

= L {t sin (6.2 t) - 6.8 sin (6.2 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)}

= L {t sin (6.2 t)} - 6.8 L {sin (6.2 t)}

L {t sin (6.2 t)} : \frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}}

L {sin (6.2 t)} : \frac{6.2}{s ^{2} + 38.44}

= \frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}} - 6.8 \cdot \frac{6.2}{s ^{2} + 38.44}

Fasse

\frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}} - 6.8 \frac{6.2}{s ^{2} + 38.44}

zusammen:

\frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}} - \frac{42.16}{s ^{2} + 38.44}

= \frac{12.4 s}{( s ^{2} + 38.44 ) ^{2}} - \frac{42.16}{s ^{2} + 38.44}

\frac{\partial}{\partial u} (2 u sin (v))

t an g e n t f (x) = x^{2} - 9, (- 4, 7)

\frac{d}{d x} (\frac{x ^{2}}{7 + x})

\int_{- \infty}^{0} \frac{1}{2 - 4 x} d x

\int_{a}^{b} f (x) d x