What is laplacetransform sin((2t)/3) ?

The answer to laplacetransform sin((2t)/3) is 6/(9s^2+4)

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laplacetransform sin((2t)/3)

laplace transform

sin (\frac{2 t}{3})

\frac{6}{9 s ^{2} + 4}

Solution steps

L {sin (\frac{2 t}{3})}

Use Laplace Transform table:

L {sin (a t)} = \frac{a}{s ^{2} + a ^{2}}

L {sin (\frac{2 t}{3})} = \frac{\frac{2}{3}}{s ^{2} + ( \frac{2}{3} ) ^{2}}

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

= \frac{6}{9 s ^{2} + 4}

What is laplacetransform sin((2t)/3) ?
The answer to laplacetransform sin((2t)/3) is 6/(9s^2+4)