The primary mirror of a large telescope can have a diameter of 10 m and a mosaic of 36 hexagonal segments with the orientation of each segment actively controlled. Suppose this unity feedback system for the mirror segments has the loop transfer function
L(s) = Gc (s)G(s) = K / s(s^2 + 2s + 5) .
(a) Find the asymptotes and sketch them in the s-plane.
(b) Find the angle of departure from the complex poles.
(c) Determine the gain when two roots lie on the imaginary axis.
(d) Sketch the root locus.

Apipe with an outside diameter of 15 cm is exposed to an ambient air and surrounding temperature of -20°c. the pipe has an outer surface temperature of 65°c and an emissivity of 0.85. if the rate of heat loss from the pipe surface is 0.95 kw per meter of length, the external convective heat transfer coefficient (h) is: (a) 12.5 w/m"k (b) 18.6 w/mk (c) 23.7 w/mk (d) 27.9 w/mk (e) 33.5 w/mk

1in2 processor chip can be modelled as an isothermal plane wall of silicon, isothermal on both sides. the power input to the bottom of the plane wall, or the processing power of the chip, often called the thermal design power (tdp), is 100w. assume the periphery is adiabatic. the silicon is 400 microns thick. the temperature at the junction, or in this case on the bottom of the isothermal plane wall, is 85°c. what is the top surface temperature, assuming that the only mode of heat transfer is conduction

Cold water (cp=4180j/kg k) leadıng to a shower enters a thin-walled double-pipe heat transfer at 15c at a rate of 0.25kg/s and is heated to 45c by hot water (cp=4190j/kg k) that enters at 100c at the rate of 3kg/s. if the overall heat transfer coefficient is 950w /m2 k , determıne the rate of heat transfer and the heat transfer surface area of the heat exchanger using e - ntu method