What is laplacetransform e^{3t}sin(2t) ?

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

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

laplace transform

e^{3 t} sin (2 t)

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

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