What is laplacetransform 4e^{-3t}cos(2t) ?

The answer to laplacetransform 4e^{-3t}cos(2t) is (4(s+3))/((s+3)^2+4)

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laplacetransform 4e^{-3t}cos(2t)

laplace transform

4 e^{- 3 t} cos (2 t)

\frac{4 ( s + 3 )}{( s + 3 ) ^{2} + 4}

Solution steps

L {4 e^{- 3 t} 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)}

= 4 L {e^{- 3 t} cos (2 t)}

L {e^{- 3 t} cos (2 t)} : \frac{s + 3}{( s + 3 ) ^{2} + 4}

= 4 \cdot \frac{s + 3}{( s + 3 ) ^{2} + 4}

Refine

4 \frac{s + 3}{( s + 3 ) ^{2} + 4} : \frac{4 ( s + 3 )}{( s + 3 ) ^{2} + 4}

= \frac{4 ( s + 3 )}{( s + 3 ) ^{2} + 4}

t \to 0 lim (\frac{9}{t} - \frac{9}{t ^{2} + t})

(y - x) y^{^{'}} = y - x + 3

\int \frac{1}{1 + w ^{2}} d w

\frac{d}{d x} (2 1 + x^{2} + 1)

x \to 3 lim (ln (x^{2} - 9))

What is laplacetransform 4e^{-3t}cos(2t) ?
The answer to laplacetransform 4e^{-3t}cos(2t) is (4(s+3))/((s+3)^2+4)