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Consider an even polynomial $p(s)$ given by \[ p(s) = s^4 + 5s^2 + 4 + K, \] where $K$ is an unknown real parameter. The complete range of $K$ for which $p(s)$ has all its roots on the imaginary axis is ________________.
  • GATE EC - 2022
  • GATE EC
  • Control Systems
  • Root Locus
The root-locus plot of a closed-loop system with unity negative feedback and transfer function $KG(s)$ in the forward path is shown in the figure. Note that $K$ is varied from 0 to $\infty$. Select the transfer function $G(s)$ that results in the shown root-locus.
  • GATE EC - 2022
  • GATE EC
  • Control Systems
  • Root Locus