What is laplacetransform e^{2t}sin(j)(2t) ?

The answer to laplacetransform e^{2t}sin(j)(2t) is (2sin(j))/((s-2)^2)

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laplacetransform e^{2t}sin(j)(2t)

laplace transform

e^{2 t} sin (j) (2 t)

\frac{2 sin ( j )}{( s - 2 ) ^{2}}

Solution steps

L {e^{2 t} sin (j) (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)}

= sin (j) \cdot 2 L {e^{2 t} t}

L {e^{2 t} t} : \frac{1}{( s - 2 ) ^{2}}

= sin (j) \cdot 2 \cdot \frac{1}{( s - 2 ) ^{2}}

Refine

sin (j) 2 \frac{1}{( s - 2 ) ^{2}} : \frac{2 sin ( j )}{( s - 2 ) ^{2}}

= \frac{2 sin ( j )}{( s - 2 ) ^{2}}

What is laplacetransform e^{2t}sin(j)(2t) ?
The answer to laplacetransform e^{2t}sin(j)(2t) is (2sin(j))/((s-2)^2)