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Beliebt Rechnen >

laplacetransform sin(t)cos(t)

Lösung

laplace transformation

sin (t) cos (t)

Lösung

\frac{1}{s ^{2} + 4}

Schritte zur Lösung

L {sin (t) cos (t)}

Verwende die folgenden Identitäten:

cos (x) sin (x) = sin (2 x) \frac{1}{2}

= L {sin (2 t) \frac{1}{2}}

Verwende die konstante Multiplikationseigenschaft der Laplace-Transformation:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= \frac{1}{2} L {sin (2 t)}

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

= \frac{1}{2} \cdot \frac{2}{s ^{2} + 4}

Fasse

\frac{1}{2} \frac{2}{s ^{2} + 4}

zusammen:

\frac{1}{s ^{2} + 4}

= \frac{1}{s ^{2} + 4}

Beliebte Beispiele

(\partial)/(\partial x)(5xye^{(x+y)})

\frac{\partial}{\partial x} (5 x y e^{(x + y)})

derivative of 2x+(4x/(3x-1))

\frac{d}{d x} (2 x + \frac{4 x}{3 x - 1})

tangent f(x)=(4x)/(x^2-5),\at x=3

t an g e n t f (x) = \frac{4 x}{x ^{2} - 5}, at x = 3

integral of 1/(xsqrt(x^2-9))

\int \frac{1}{x x ^{2} - 9} d x

integral from 0 to 2 of 1

\int_{0}^{2} 1