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I am studying Control Theory from Ogata. My math is a little rusty, so this is a math question about Frequency Domain Analysis.

Check this page - http://www.flickr.com/photos/66943862@N06/6337116280/sizes/l/in/photostream/ [Broken]

I get everything upto Equation 8-4

However I don't get the line after that.

The line "where the constant a can be evaluated from Equation (8-2) as follows"

And they write the value of a.

How is

a = G(s) (ωX) /(s^2 + ω^2).

How do they arrive at this value of a?

Can someone help?

And why did they substitute s = -jω after that?

Check this page - http://www.flickr.com/photos/66943862@N06/6337116280/sizes/l/in/photostream/ [Broken]

I get everything upto Equation 8-4

However I don't get the line after that.

The line "where the constant a can be evaluated from Equation (8-2) as follows"

And they write the value of a.

How is

a = G(s) (ωX) /(s^2 + ω^2).

How do they arrive at this value of a?

Can someone help?

And why did they substitute s = -jω after that?

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