What is laplacetransform 1/2 cos(2t) ?

The answer to laplacetransform 1/2 cos(2t) is s/(2(s^2+4))

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laplacetransform 1/2 cos(2t)

laplace transform

\frac{1}{2} cos (2 t)

\frac{s}{2 ( s ^{2} + 4 )}

Solution steps

L {\frac{1}{2} cos (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)}

= \frac{1}{2} L {cos (2 t)}

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

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

Refine

\frac{1}{2} \frac{s}{s ^{2} + 4} : \frac{s}{2 ( s ^{2} + 4 )}

= \frac{s}{2 ( s ^{2} + 4 )}

\int \frac{1}{u a ^{2} - u ^{2}} d u

\frac{\partial}{\partial z} (cos (x yz))

\frac{d y}{d t} = 1.4 y

\int \frac{1}{- x ^{2} - 1} d x

What is laplacetransform 1/2 cos(2t) ?
The answer to laplacetransform 1/2 cos(2t) is s/(2(s^2+4))