What is laplacetransform e^{-0.75t}*cos(4t) ?

The answer to laplacetransform e^{-0.75t}*cos(4t) is (s+0.75)/((s+0.75)^2+16)

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laplacetransform e^{-0.75t}*cos(4t)

laplace transform

e^{- 0.75 t} \cdot cos (4 t)

\frac{s + 0.75}{( s + 0.75 ) ^{2} + 16}

Solution steps

L {e^{- 0.75 t} cos (4 t)}

Apply transform rule:

L {f (t)} = F (s)

then

L {e^{a t} f (t)} = F (s - a)

For

e^{- 0.75 t} cos (4 t) : f (t) = cos (4 t), a = - 0.75

= L {cos (4 t)} (s + 0.75)

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

= \frac{( s + 0.75 )}{( s + 0.75 ) ^{2} + 16}

= \frac{s + 0.75}{( s + 0.75 ) ^{2} + 16}

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What is laplacetransform e^{-0.75t}*cos(4t) ?
The answer to laplacetransform e^{-0.75t}*cos(4t) is (s+0.75)/((s+0.75)^2+16)