What is laplacetransform 2sin(3t) ?

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

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laplacetransform 2sin(3t)

laplace transform

2 sin (3 t)

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

Solution steps

L {2 sin (3 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 (3 t)}

L {sin (3 t)} : \frac{3}{s ^{2} + 9}

= 2 \cdot \frac{3}{s ^{2} + 9}

Refine

2 \frac{3}{s ^{2} + 9} : \frac{6}{s ^{2} + 9}

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

x \to 1 lim (a x + b)

\frac{d}{d x} (3 x - 7)

\int \frac{1}{x e ^{- x}} d x

\frac{d}{d x} ((5 x^{3} + 3) (x^{4} - 2 x))

t e^{2 t} sin (t)

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