Control System Equations

I need mathematical justification and proof on the breakaway point in root locus SECOND ORDER SYSTEM ONLY

The proof must show why always the break away point is in the middle also the justification and the proof must have a mathematical equation and proof on the general concept of the road locus of second order system only

I will attach a picture to show what I mean

Skills: Electrical Engineering, Electronics, Engineering, Mathematics, Matlab and Mathematica

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