What is laplacetransform 3tcos(2t) ?

The answer to laplacetransform 3tcos(2t) is -(3(-s^2+4))/((s^2+4)^2)

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laplacetransform 3tcos(2t)

laplace transform

3 t cos (2 t)

- \frac{3 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

Solution steps

L {3 t cos (2 t)}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= 3 L {t cos (2 t)}

L {t cos (2 t)} : - \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}}

= 3 (- \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}})

Refine

3 (- \frac{- s ^{2} + 4}{( s ^{2} + 4 ) ^{2}}) : - \frac{3 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

= - \frac{3 ( - s ^{2} + 4 )}{( s ^{2} + 4 ) ^{2}}

What is laplacetransform 3tcos(2t) ?
The answer to laplacetransform 3tcos(2t) is -(3(-s^2+4))/((s^2+4)^2)