What is laplacetransform 3cos(3t) ?

The answer to laplacetransform 3cos(3t) is (3s)/(s^2+9)

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laplacetransform 3cos(3t)

laplace transform

3 cos (3 t)

\frac{3 s}{s ^{2} + 9}

Solution steps

L {3 cos (3 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)}

= 3 L {cos (3 t)}

L {cos (3 t)} : \frac{s}{s ^{2} + 9}

= 3 \cdot \frac{s}{s ^{2} + 9}

Refine

3 \frac{s}{s ^{2} + 9} : \frac{3 s}{s ^{2} + 9}

= \frac{3 s}{s ^{2} + 9}

y^{^{''}} + 8 y^{^{'}} + 19 y = 0, y (0) = 3, y^{^{'}} (0) = - 4

y^{^{'''}} - 2 y^{^{''}} - 12 y^{^{'}} + 16 y = 0

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

\frac{3}{( 2 s ^{2} + 8 s + 10 )}

\int \frac{1}{x ^{2} - 8 x + 1} d x

What is laplacetransform 3cos(3t) ?
The answer to laplacetransform 3cos(3t) is (3s)/(s^2+9)