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)

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.