Robotics Control System

Draw the root locus for $$G(s)H(s) = \frac{k}{s(s^2 + 2s + 5)}$$ and find the range of 'k' for stability.

Find the number of poles in the left half-plane, the right half-plane, and on the $j\omega$-axis for the characteristic equation $$p(s) = 2s^5 + 3s^4 + 2s^3 + 3s^2 + 2s + 1 = 0$$

Draw the Bode plot for the transfer function and find the P.M. & G.M.
$$G(s) = \frac{200(s + 2)}{s(s^2 + 10s + 100)}$$