# Controlled system - Closed loop system

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I have this assignment (First problem - exercise 2 - dias 7)
http://site.iugaza.edu.ps/bhamed/files/2010/02/L4-Root-Locus.ppt

Which i am having some problems solving.
I am stuck at B)

So far i tried to solve the problem, by calculating the distance from origin to the breakaway point, by diff. , and then using Tan(ArcCos(0.707)) * breakaway to get the jw coordinate for the pole.

With the σ and jw for the pole, I then solve K2 for the charactic equation.

where i get the value K2 = 6.23475*10^6
calc: showing ch. eq => Redbox indicate S, and bluebox indicate jw value
http://snag.gy/Fkz26.jpg

Jw calculation: http://snag.gy/oZ4u9.jpg
But according to solution manual it should be 81000..

I don't see where i am going wrong.

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