# 48.&nbsp; The characteristic equation of a uni...

48.  The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.

The constant damping ratio line, for $\varsigma$=0.5 intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________ .