What is laplacetransform t*cos(kt) ?

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

Popular >

laplacetransform t*cos(kt)

laplace transform

t \cdot cos (k t)

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

Solution steps

L {t cos (k t)}

Use Laplace Transform table:

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

For

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

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

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

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

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

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

\int \frac{1}{9 x - 4} d x

\int \frac{x ^{2} - 2 x}{x ^{3} - 3 x ^{2} + 1} d x

\frac{d}{d x} (e^{s i n (x)} \cdot cos (sin (x)))

y^{^{'}} - \frac{8}{x} y = \frac{y ^{4}}{x ^{18}}

\int X^{2} d X

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