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

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

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laplacetransform 3sin(sqrt(2)t)

laplace transform

3 sin (2 t)

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

Solution steps

L {3 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)}

= 3 L {sin (2 t)}

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

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

Refine

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

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

\int - 2 x^{- 4} d x

d er i v a t i v e f (x) = (\frac{5 ^{3 x^{7}}}{8 x ^{2}})^{4}

\int \frac{x - 3}{x ^{2} - 12 x + 36} d x

n = 1 \sum \infty \frac{n}{n + 3}

t an g e n t f (x) = (2 + 4 x) (5 - 4 x), at x = 1

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