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Beliebt Rechnen >

laplacetransform 5cos(2t)-3sin(3t)

Lösung

laplace transformation

5 cos (2 t) - 3 sin (3 t)

Lösung

\frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

Schritte zur Lösung

L {5 cos (2 t) - 3 sin (3 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)}

= 5 L {cos (2 t)} - 3 L {sin (3 t)}

L {cos (2 t)} : \frac{s}{s ^{2} + 4}

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= 5 \cdot \frac{s}{s ^{2} + 4} - 3 \cdot \frac{3}{s ^{2} + 9}

Fasse

5 \frac{s}{s ^{2} + 4} - 3 \frac{3}{s ^{2} + 9}

zusammen:

\frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

= \frac{5 s}{s ^{2} + 4} - \frac{9}{s ^{2} + 9}

Beliebte Beispiele

y^{''}-6/x y^'+(10)/(x^2)y=0

y^{^{''}} - \frac{6}{x} y^{^{'}} + \frac{10}{x ^{2}} y = 0

limit as h approaches 0 of (sqrt(h+5)-sqrt(5))/h

h \to 0 lim (\frac{h + 5 - 5}{h})

tangent y= 2/(1-3x),\at x=-1

t an g e n t y = \frac{2}{1 - 3 x}, at x = - 1

integral of (x+8)/(x^2+9)

\int \frac{x + 8}{x ^{2} + 9} d x

integral of 1/(sqrt(x^2-400))

\int \frac{1}{x ^{2} - 400} d x