The open-loop transfer function of a robot arm drive might be approximated G(s) H(s)=\frac{2 K(s+0.5 a)}{(s+3)\left(s^{2}+4 s+8\right)}, a, K>0 Use the Routh-Hurwitz criterion to show that for sufficiently small a,

the system is stable for all(positive) values of K. Let a = 15. Show that the system becomes unstable for sufficiently large K, and find all the roots of the system when it is marginally stable. Mention the frequency of oscillation in Hz. For the values in ii), where the system is marginally stable, plot the system's step response (assume unity gain feedback), and show that there is a sustained oscillation at the frequency in ii) A sample is shown below