5.9 A U-tube manometer that is open to the atmosphere has a manometric fluid with the following characteristics: L = 0.8 m p = 2000 kg/m u= 0.002 kg/(m s). You are asked to design the tube diameter in the range 0.001 m to 0.010 m, so as to achieve rise time less than 0.5 s overshoot less than 50%. Propose a final design based on the information that sinusoidal disturbances with amplitude of 10 000 Pa at various frequencies are common for the system under study. Assume that g 10 m/s and that the design of an underdamped system has been selected (i.e. 0 < < < 1). For all permissible designs, use MATLAB to generate (a) the Bode diagram, (b) the step response for a step change in the measured pressure of 10 000 Pa, (c) the ramp response for a ramp input u(t)=10 000t Pa that lasts for 2 s and (d) the pulse response for a pulse of 1 000 000 Pa that lasts for 0.01 s.