The question pertains to engineering and involves drawing a Nyquist plot for a given transfer function and discussing the effects of varying gain on closed-loop stability using the Nyquist stability criterion.
The question involves creating an open loop Nyquist plot and discussing closed-loop stability for different values of a gain k. This task is rooted in control systems, a sub-discipline of engineering, where Nyquist plots are used to determine the stability of a system based on the path a function takes in the complex plane as frequency varies from zero to infinity.
For a transfer function gp(s), different values of gain k will affect the location of poles in the transfer function and consequently the stability of the closed-loop system. Closed-loop stability can be assessed by the Nyquist stability criterion, which relates the number of clockwise encirclements around the point -1+0j to the number of poles in the right half-plane (RHP) that are not cancelled by zeros in the system.