What is laplacetransform te^{-3t}sin(5t) ?

The answer to laplacetransform te^{-3t}sin(5t) is (5(2s+6))/((s^2+6s+34)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

laplacetransform te^{-3t}sin(5t)

laplace transform

t e^{- 3 t} sin (5 t)

\frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

Solution steps

L {e^{- 3 t} t sin (5 t)}

Use Laplace Transform table:

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

For

t e^{- 3 t} sin (5 t) : f (t) = e^{- 3 t} sin (5 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {e^{- 3 t} sin (5 t)})

L {e^{- 3 t} sin (5 t)} : \frac{5}{( s + 3 ) ^{2} + 25}

\frac{d}{d s} (\frac{5}{( s + 3 ) ^{2} + 25}) = - \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

= (- 1)^{1} (- \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}})

= \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

\int \frac{2 x - 1}{x ^{2} + 4} d x

\int \frac{4}{5} x^{3} d x

i (t)

\int \frac{1}{( x ^{2} + 9 ) ^{\frac{3}{2}}} d x

\int cos (4 t) d t

What is laplacetransform te^{-3t}sin(5t) ?
The answer to laplacetransform te^{-3t}sin(5t) is (5(2s+6))/((s^2+6s+34)^2)