What is laplacetransform 3e^{-7t}cos(t/3+pi/3) ?

The answer to laplacetransform 3e^{-7t}cos(t/3+pi/3) is (9sqrt(3)(sqrt(3)(s+7)-1))/(2(9(s+7)^2+1))

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laplacetransform 3e^{-7t}cos(t/3+pi/3)

laplace transform

3 e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})

\frac{9 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )}

Solution steps

L {3 e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})}

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)}

= 3 L {e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})}

L {e^{- 7 t} cos (\frac{t}{3} + \frac{π}{3})} : \frac{3 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )}

= 3 \cdot \frac{3 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )}

Refine

3 \frac{3 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )} : \frac{9 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )}

= \frac{9 3 ( 3 ( s + 7 ) - 1 )}{2 ( 9 ( s + 7 ) ^{2} + 1 )}

\frac{d y}{d x - y ^{2}} = 36

x \to 0 lim (\frac{cos ( 4 x ) - 1}{x})

\frac{\partial}{\partial y} (2 x sin (y))

v \to 4 + lim (\frac{4 - v}{∣ 4 - v ∣})

\frac{\partial}{\partial x} (x^{2} + 5)

What is laplacetransform 3e^{-7t}cos(t/3+pi/3) ?
The answer to laplacetransform 3e^{-7t}cos(t/3+pi/3) is (9sqrt(3)(sqrt(3)(s+7)-1))/(2(9(s+7)^2+1))