What is laplacetransform sin(2t)*cos(2t) ?

The answer to laplacetransform sin(2t)*cos(2t) is 2/(s^2+16)

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laplacetransform sin(2t)*cos(2t)

laplace transform

sin (2 t) \cdot cos (2 t)

\frac{2}{s ^{2} + 16}

Solution steps

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

Rewrite using trig identities

L {\frac{1}{2} sin (4 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{1}{2} L {sin (4 t)}

L {sin (4 t)} : \frac{4}{s ^{2} + 16}

= \frac{1}{2} \cdot \frac{4}{s ^{2} + 16}

Refine

\frac{1}{2} \frac{4}{s ^{2} + 16} : \frac{2}{s ^{2} + 16}

= \frac{2}{s ^{2} + 16}

y^{^{''}} + y^{^{'}} = 2

f (x) = 2 x + 1, at x = 4

\frac{d}{d t} (\frac{y}{t} - (\frac{y}{t})^{2})

\int_{1}^{2} \frac{4}{x} - \frac{16}{x ^{2}} d x

\frac{\partial}{\partial y} (y - e^{- 2 x^{2} y})

What is laplacetransform sin(2t)*cos(2t) ?
The answer to laplacetransform sin(2t)*cos(2t) is 2/(s^2+16)