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

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

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laplacetransform 3/2 sin(2t)

laplace transform

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

\frac{3}{s ^{2} + 4}

Solution steps

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

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)}

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

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

= \frac{3}{2} \cdot \frac{2}{s ^{2} + 4}

Refine

\frac{3}{2} \frac{2}{s ^{2} + 4} : \frac{3}{s ^{2} + 4}

= \frac{3}{s ^{2} + 4}

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