For each of the following open-loop transfer functions, construct a Bode plot for \(K=1\) using the MATLAB command bode. Estimate the GM, PM, and their associated crossover frequencies from the plot. Verify the results using the MATLAB command margin. Determine the stability of the corresponding closedloop system.

a. \(K G(s)=\frac{K}{s\left(s^{2}+2 s+64\right)}\)

b. \(K G(s)=K \frac{1000}{(s+8)\left(s^{2}+2 s+4\right)}\)

c. \(K G(s)=K \frac{s+0.1}{s(s+5)^{2}}\)

d. \(K G(s)=K \frac{1}{(s+5)(s+0.5)^{2}}\)