What is laplacetransform sqrt(2)sin(sqrt(2)t) ?

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

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laplacetransform sqrt(2)sin(sqrt(2)t)

laplace transform

2 sin (2 t)

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

Solution steps

L {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)}

= 2 L {sin (2 t)}

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

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

Refine

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

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

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