What is laplacetransform t*cos(3t) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

laplacetransform t*cos(3t)

laplace transform

t \cdot cos (3 t)

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

Solution steps

L {t cos (3 t)}

Use Laplace Transform table:

L {t^{k} f (t)} = (- 1)^{k} \frac{d ^{k}}{d s ^{k}} (L {f (t)})

For

t cos (3 t) : f (t) = cos (3 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {cos (3 t)})

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

\frac{d}{d s} (\frac{s}{s ^{2} + 9}) = \frac{- s ^{2} + 9}{( s ^{2} + 9 ) ^{2}}

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

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

\frac{d}{d x} (x^{5} e^{4 x})

\frac{d}{d x} ((5 x - 1)^{3} (x^{2} + 1)^{5})

t an g e n t f (x) = 8 - 2 x^{2}, at x = 0

\int x 2 x + 5 d x

s l o p e f (x) = 25 x^{\frac{4}{5}}

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