What is laplacetransform 1-cos(7t) ?

The answer to laplacetransform 1-cos(7t) is (49)/(s(s^2+49))

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laplacetransform 1-cos(7t)

laplace transform

1 - cos (7 t)

\frac{49}{s ( s ^{2} + 49 )}

Solution steps

L {1 - cos (7 t)}

Use the linearity property of Laplace Transform:

For functions

f (t), g (t)

and constants

a, b : L {a \cdot f (t) + b \cdot g (t)} = a \cdot L {f (t)} + b \cdot L {g (t)}

= L {1} - L {cos (7 t)}

L {1} : \frac{1}{s}

L {cos (7 t)} : \frac{s}{s ^{2} + 49}

= \frac{1}{s} - \frac{s}{s ^{2} + 49}

Simplify

\frac{1}{s} - \frac{s}{s ^{2} + 49} : \frac{49}{s ( s ^{2} + 49 )}

= \frac{49}{s ( s ^{2} + 49 )}

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

x \to 0 lim ((e^{x} + 1)^{\frac{1}{x}})

x = y (y - 13), x = - y (y - 13)

\frac{d}{d x} (\frac{e ^{x}}{5 x ^{2}})

\frac{d}{d x} (e^{x} sin (x) + cos (x) e^{x})

What is laplacetransform 1-cos(7t) ?
The answer to laplacetransform 1-cos(7t) is (49)/(s(s^2+49))