Shown below is the feedback system for this problem.  The system has an adjustable gain amplifier with a gain, K, and a system with a transfer function, G(s)

        The transfer function for the system being controlled - the plant - is given by:

You need to investigate the behavior of this system.

Plot the locus of poles of the closed loop system as a function of gain.

• Plot the locus of poles of the closed loop system as a function of gain.
• Clearly indicate any points where poles leave the real axis or where they rejoin the real axis.
• Show the value of the gain, K, where those points occur.