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

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

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

laplace transform

e^{2 t} sin (2 t j)

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

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

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

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