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Not a homework problem exactly, but in an EE textbook I saw something to the following effect:

To obtain the time domain behavior for [tex]\frac{s}{s^2+\frac{\omega_0}{Q} + {\omega_0}^2}[/tex] the following Laplace transforms are combined to cancel the term in the numerator:

[tex]\frac{1}{(s-\alpha)^2+b^2} = \frac{1}{b}e^{\alpha t}sin(bt)[/tex]

and

[tex]\frac{s+\alpha}{(s-a)^2 + b^2} = e^{\alpha t}cos(bt)[/tex]

I may just be tired, but I'm having a lot of trouble seeing how those two Laplace transforms were algebraically combined to get "s" alone in the numerator. Any hint would be appreciated.

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# Homework Help: Laplace transform combination

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