What is laplacetransform 0.5e^{-4.5t}sin(2pit) ?

The answer to laplacetransform 0.5e^{-4.5t}sin(2pit) is pi/((s+4.5)^2+4pi^2)

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laplacetransform 0.5e^{-4.5t}sin(2pit)

laplace transform

0.5 e^{- 4.5 t} sin (2 π t)

\frac{π}{( s + 4.5 ) ^{2} + 4 π ^{2}}

Solution steps

L {0.5 e^{- 4.5 t} sin (2 π 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)}

= 0.5 L {e^{- 4.5 t} sin (2 π t)}

L {e^{- 4.5 t} sin (2 π t)} : \frac{2 π}{( s + 4.5 ) ^{2} + 4 π ^{2}}

= 0.5 \cdot \frac{2 π}{( s + 4.5 ) ^{2} + 4 π ^{2}}

Refine

0.5 \frac{2 π}{( s + 4.5 ) ^{2} + 4 π ^{2}} : \frac{π}{( s + 4.5 ) ^{2} + 4 π ^{2}}

= \frac{π}{( s + 4.5 ) ^{2} + 4 π ^{2}}

\frac{d y}{d x} = 3 x - y + 4

\int \frac{( ln ( x ) ) ^{50}}{x} d x

s^{2}

(\frac{x}{x ^{2} + 1})^{^{'}}

\int cos (x) sin (x) e^{- 2 c o s (x)} d x

What is laplacetransform 0.5e^{-4.5t}sin(2pit) ?
The answer to laplacetransform 0.5e^{-4.5t}sin(2pit) is pi/((s+4.5)^2+4pi^2)