What is laplacetransform 3sin(4t+2)e^{-6t} ?

The answer to laplacetransform 3sin(4t+2)e^{-6t} is (3(sin(2)(s+6)+4cos(2)))/((s+6)^2+16)

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laplacetransform 3sin(4t+2)e^{-6t}

laplace transform

3 sin (4 t + 2) e^{- 6 t}

\frac{3 ( sin ( 2 ) ( s + 6 ) + 4 cos ( 2 ) )}{( s + 6 ) ^{2} + 16}

Solution steps

L {3 e^{- 6 t} sin (4 t + 2)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

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

= 3 L {sin (4 t + 2) e^{- 6 t}}

L {sin (4 t + 2) e^{- 6 t}} : \frac{sin ( 2 ) ( s + 6 ) + 4 cos ( 2 )}{( s + 6 ) ^{2} + 16}

= 3 \cdot \frac{sin ( 2 ) ( s + 6 ) + 4 cos ( 2 )}{( s + 6 ) ^{2} + 16}

Refine

3 \frac{sin ( 2 ) ( s + 6 ) + 4 cos ( 2 )}{( s + 6 ) ^{2} + 16} : \frac{3 ( sin ( 2 ) ( s + 6 ) + 4 cos ( 2 ) )}{( s + 6 ) ^{2} + 16}

= \frac{3 ( sin ( 2 ) ( s + 6 ) + 4 cos ( 2 ) )}{( s + 6 ) ^{2} + 16}

What is laplacetransform 3sin(4t+2)e^{-6t} ?
The answer to laplacetransform 3sin(4t+2)e^{-6t} is (3(sin(2)(s+6)+4cos(2)))/((s+6)^2+16)