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

The answer to laplacetransform e^{-4t}*cos(t) is (s+4)/((s+4)^2+1)

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

laplace transform

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

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

Solution steps

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

Apply transform rule:

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

then

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

For

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

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

L {cos (t)} : \frac{s}{s ^{2} + 1}

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

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

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What is laplacetransform e^{-4t}*cos(t) ?
The answer to laplacetransform e^{-4t}*cos(t) is (s+4)/((s+4)^2+1)