$9.$ Given the following unity$-$feedback system:

a$.$ Please sketch the root$-$locus of the system by manual computation. Determine where the root$-$locus on the real axis, and the asymptotes $($if there are any$).$ Please write the way, not just the results. Verify your answer by plotting the root$-$locus by using computer program.

b$.$ For which gain K the system will have damping ratio $0\mathrm{.}45?$ You can use computer program for this. Please show why the points with the same damping ratio in root locus plot will form a straight line.

c$.$ Find the range of gain, K $,$ for which the system is stable.