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Beliebt Rechnen >

laplacetransform e^{3t}cos(2t)

Lösung

laplace transformation

e^{3 t} cos (2 t)

Lösung

\frac{s - 3}{( s - 3 ) ^{2} + 4}

Schritte zur Lösung

L {e^{3 t} cos (2 t)}

Wende Transformationsregel an: wenn

L {f (t)} = F (s)

dann

L {e^{a t} f (t)} = F (s - a)

Für

e^{3 t} cos (2 t) : f (t) = cos (2 t), a = 3

= L {cos (2 t)} (s - 3)

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

= \frac{( s - 3 )}{( s - 3 ) ^{2} + 4}

= \frac{s - 3}{( s - 3 ) ^{2} + 4}

Beliebte Beispiele

derivative of sin^2(e^{sin^2(x}))

\frac{d}{d x} (sin^{2} (e^{s i n^{2} (x)}))

integral of 3xcos^3(x^2+2)

\int 3 x cos^{3} (x^{2} + 2) d x

tangent f(x)=x^2,\at m(x)=-1/2

t an g e n t f (x) = x^{2}, at m (x) = - \frac{1}{2}

derivative of sqrt(r^2-8x^2)

\frac{d}{d x} (r^{2} - 8 x^{2})

integral of x(x+4)^{-3/2}

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