What is laplacetransform 3sin(sqrt(2)t)-3cos(sqrt(2)t) ?

The answer to laplacetransform 3sin(sqrt(2)t)-3cos(sqrt(2)t) is (3sqrt(2))/(s^2+2)-(3s)/(s^2+2)

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laplacetransform 3sin(sqrt(2)t)-3cos(sqrt(2)t)

laplace transform

3 sin (2 t) - 3 cos (2 t)

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

Solution steps

L {3 sin (2 t) - 3 cos (2 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

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

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

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

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

Refine

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

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

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