# Transient Response and s-plane root location

A second-order system has the closed-loop transfer function T(s)=Y(s)/R(s). The system specifications for a unit step input is as follows:

I managed to solve the problem until this step. But I am stuck at solving the permissible area for the poles in the s-plane as per the question mentioned in the given image.

• Why are you stuck at this final hurdle. Explain. – Andy aka Aug 30 at 6:59
• Sketch regions of the s-plane that satisfy each of the three criteria, defined by your equations. That will define the region that satisfies all three concurrently. – Chu Aug 30 at 11:06