What is laplacetransform cos^2(21t) ?

The answer to laplacetransform cos^2(21t) is 1/(2s)+s/(2(s^2+1764))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform cos^2(21t)

laplace transform

cos^{2} (21 t)

\frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 1764 )}

Solution steps

L {cos^{2} (21 t)}

Rewrite using trig identities

L {\frac{1}{2} + \frac{1}{2} cos (42 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 {\frac{1}{2}} + \frac{1}{2} L {cos (42 t)}

L {\frac{1}{2}} : \frac{1}{2 s}

L {cos (42 t)} : \frac{s}{s ^{2} + 1764}

= \frac{1}{2 s} + \frac{1}{2} \cdot \frac{s}{s ^{2} + 1764}

Refine

\frac{1}{2 s} + \frac{1}{2} \frac{s}{s ^{2} + 1764} : \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 1764 )}

= \frac{1}{2 s} + \frac{s}{2 ( s ^{2} + 1764 )}

y = 2 sin (x), 0, at x = 0

4 x^{2} - 4, x^{4} - 1

x \to \infty lim (- \frac{9}{x})

f (x) = e^{2 x^{2}}

y = 6 x - x^{2}, y = - 2 x

What is laplacetransform cos^2(21t) ?
The answer to laplacetransform cos^2(21t) is 1/(2s)+s/(2(s^2+1764))