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

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

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laplacetransform 1/2+1/2 cos(2t)

laplace transform

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

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

Solution steps

L {\frac{1}{2} + \frac{1}{2} 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)}

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

L {\frac{1}{2}} : \frac{1}{2 s}

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

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

Refine

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

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

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