What is laplacetransform tsin(0.32t) ?

The answer to laplacetransform tsin(0.32t) is (0.64s)/((s^2+0.1024)^2)

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laplacetransform tsin(0.32t)

laplace transform

t sin (0.32 t)

\frac{0.64 s}{( s ^{2} + 0.1024 ) ^{2}}

Solution steps

L {t sin (0.32 t)}

Use Laplace Transform table:

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

For

t sin (0.32 t) : f (t) = sin (0.32 t), k = 1

= (- 1)^{1} \frac{d}{d s} (L {sin (0.32 t)})

L {sin (0.32 t)} : \frac{0.32}{s ^{2} + 0.1024}

\frac{d}{d s} (\frac{0.32}{s ^{2} + 0.1024}) = - \frac{0.64 s}{( s ^{2} + 0.1024 ) ^{2}}

= (- 1)^{1} (- \frac{0.64 s}{( s ^{2} + 0.1024 ) ^{2}})

= \frac{0.64 s}{( s ^{2} + 0.1024 ) ^{2}}

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What is laplacetransform tsin(0.32t) ?
The answer to laplacetransform tsin(0.32t) is (0.64s)/((s^2+0.1024)^2)