laplacetransform 3sin(5t+45)

Lösung

laplace transformation

3 sin (5 t + 45)

\frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

Schritte zur Lösung

L {3 sin (5 t + 45)}

Verwende die konstante Multiplikationseigenschaft der Laplace-Transformation:

For function

f (t)

and constant

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

= 3 L {sin (5 t + 45)}

L {sin (5 t + 45)} : \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25}

= 3 \cdot \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25}

Fasse

3 \frac{sin ( 45 ) s + 5 cos ( 45 )}{s ^{2} + 25}

zusammen:

\frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

= \frac{3 ( sin ( 45 ) s + 5 cos ( 45 ) )}{s ^{2} + 25}

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