What is laplacetransform t*sin(t) ?

The answer to laplacetransform t*sin(t) is (2s)/((s^2+1)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform t*sin(t)

laplace transform

t \cdot sin (t)

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

Solution steps

L {t sin (t)}

Use Laplace Transform table:

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

For

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

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

L {sin (t)} : \frac{1}{s ^{2} + 1}

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

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

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

\frac{d}{d x} (sin (2 x) + 3 ln (e) + 4 x)

(4, 2), (3, - 1)

\frac{\partial}{\partial θ} (cos^{2} (θ))

\int (cos (θ))^{3} d θ

\int_{0}^{\frac{π}{3}} x sin (x + y) d y

What is laplacetransform t*sin(t) ?
The answer to laplacetransform t*sin(t) is (2s)/((s^2+1)^2)