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Beliebt Rechnen >

laplacetransform 7sin(4t+8)+3cos(4t-2)

Lösung

laplace transformation

7 sin (4 t + 8) + 3 cos (4 t - 2)

Lösung

\frac{7 ( sin ( 8 ) s + 4 cos ( 8 ) )}{s ^{2} + 16} + \frac{3 ( cos ( 2 ) s + 4 sin ( 2 ) )}{s ^{2} + 16}

Schritte zur Lösung

L {7 sin (4 t + 8) + 3 cos (4 t - 2)}

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)}

= 7 L {sin (4 t + 8)} + 3 L {cos (4 t - 2)}

L {sin (4 t + 8)} : \frac{sin ( 8 ) s + 4 cos ( 8 )}{s ^{2} + 16}

L {cos (4 t - 2)} : \frac{cos ( 2 ) s + 4 sin ( 2 )}{s ^{2} + 16}

= 7 \cdot \frac{sin ( 8 ) s + 4 cos ( 8 )}{s ^{2} + 16} + 3 \cdot \frac{cos ( 2 ) s + 4 sin ( 2 )}{s ^{2} + 16}

Fasse

7 \frac{sin ( 8 ) s + 4 cos ( 8 )}{s ^{2} + 16} + 3 \frac{cos ( 2 ) s + 4 sin ( 2 )}{s ^{2} + 16}

zusammen:

\frac{7 ( sin ( 8 ) s + 4 cos ( 8 ) )}{s ^{2} + 16} + \frac{3 ( cos ( 2 ) s + 4 sin ( 2 ) )}{s ^{2} + 16}

= \frac{7 ( sin ( 8 ) s + 4 cos ( 8 ) )}{s ^{2} + 16} + \frac{3 ( cos ( 2 ) s + 4 sin ( 2 ) )}{s ^{2} + 16}

Beliebte Beispiele

limit as x approaches 1 of 1-x-[x]

x \to 1 lim (1 - x - [x])

derivative of (2x-3/(x^2-1))

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

integral of (6x+y)

\int (6 x + y) d x

xy'+(1+xcot(x))y=0

x y^{'} + (1 + x cot (x)) y = 0

tangent f(x)=tan(3x),\at x= pi/9

t an g e n t f (x) = tan (3 x), at x = \frac{π}{9}