Q2/A) The system is shown in the next page: 1. Find the value of (m) when the damping ratio () is (0.7). Then obtain the maximum over shoot, peak time, rise time, and settling time. 2. Determine (on) and (C) when (m) equal zero. 3. Calculate the value of steady state error for this system if the input is a unit ramp. X(s) 250 Y(s) S(S+10) 3m S + 1

A copper sphere initially at a uniform temperature To is immersed in a fluid. Electric heaters are placed in the fluid and controlled so that the temperature of the fluid follows a periodic variation given by Too - Tm A sin wt where Tm = time-average mean fluid temperature A = amplitude of temperature wave @= frequency Derive an expression for the temperature of the sphere as a function of time and the heat-transfer coefficient from the fluid to the sphere. Assume that the temperares of the sphere and fluid are uniform at any instant so that the lumped-capacity method of analysis may be used.

Q2/B) Is the following system under damping? If yes, determine the maximum over shoot, peak time, rise time, and the settling time. X(s) + 2S S2 8S+16 0.1S+1 S+4 Y(s) S

What is the huge benefit of having the pump upstream of the eluent generator rather than downstream of the eluent generator? Hide hint for Question Consider what would be going through the pump in each case.