What is laplacetransform 10cos(8t)+14sin(8t) ?

The answer to laplacetransform 10cos(8t)+14sin(8t) is (10s)/(s^2+64)+(112)/(s^2+64)

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laplacetransform 10cos(8t)+14sin(8t)

laplace transform

10 cos (8 t) + 14 sin (8 t)

\frac{10 s}{s ^{2} + 64} + \frac{112}{s ^{2} + 64}

Solution steps

L {10 cos (8 t) + 14 sin (8 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)}

= 10 L {cos (8 t)} + 14 L {sin (8 t)}

L {cos (8 t)} : \frac{s}{s ^{2} + 64}

L {sin (8 t)} : \frac{8}{s ^{2} + 64}

= 10 \cdot \frac{s}{s ^{2} + 64} + 14 \cdot \frac{8}{s ^{2} + 64}

Refine

10 \frac{s}{s ^{2} + 64} + 14 \frac{8}{s ^{2} + 64} : \frac{10 s}{s ^{2} + 64} + \frac{112}{s ^{2} + 64}

= \frac{10 s}{s ^{2} + 64} + \frac{112}{s ^{2} + 64}

x \to 1 lim (2 x^{\frac{3}{2}} - 3 x^{2})

\frac{d}{d x} (7 x^{2} + 8 x)

f (x) = 3 x^{2} + 2 x, at p (- 1, 5)

\frac{d}{d x} (cos (4 x) \cdot 4)

n = 1 \sum \infty \frac{2 n ^{2}}{n !}

What is laplacetransform 10cos(8t)+14sin(8t) ?
The answer to laplacetransform 10cos(8t)+14sin(8t) is (10s)/(s^2+64)+(112)/(s^2+64)