For each of the following loop transfer function f(s), find the portion of the root locus on the real axis, asymptotes, the arrival and departure angles at any complex zero or pole, and the frequency of any imaginary-axis crossing. plot the sketch of the root locus based on above findings. verify your results using matlab. submit plots of your hand sketches and the matlab results.
a. f(s)=- s(s+1)(s +5)(8 +10)
b. f(s)=; s +2 s(s+1)(3+5)(8+10) (s+2)(s+6)
c. f(s)= (+1)(3+5)(s+10)

Consider a 1.2 meter high and 2 meter wide glass window whose thickness is 6 mm and thermal conductivity is 0.78 w/m °c. the room temperature is maintained at 24 °c, while the outdoor temperature is -5 °c. the convective heat transfer coefficients on the inner and outer surfaces of the window are 10 w/m2 °c and 25 w/m2 °c respectively. (a) draw the thermal resistance network, etermine the steady rate of heat transfer t e glass window (c) determine the temperature of the inner surface of the window