Suppose a liquid-level system (see Lecture 12) has a cross-sectional area of 2 m^2 and a flow resistance of 40 m/(m^3 /t)(this unit reflects that the resistance is defined as

the ratio of a change in height to the corresponding change in volumetric outlet flow). The tank is initially empty, and we assume it is tall enough to not overflow in this problem. a) Based on the transfer function from Lecture 13, find the differential equation relating the inlet and outlet volumetric flow rates, as a function of time. bị What is the time constant of this system. in s? c) Suppose water is poured into the tank at a constant rate of 0.1 m³/s. What will the outlet flow rate be, in m/s, after a duration of two time constants? d) Suppose water is poured into the tank at a constant rate of 0.2 m^2/s. At what time, in s, Will the outlet flow rate reach 0.1 m^3/s? e) Suppose the outlet flow from this system is directed into a second liquid-level system with the same parameters, forming a second-order system. What is the damping ratio of the combined system? f) Is the combined system undamped, underdamped, or overdamped?