Problem $2.(40$ pts$)$ For the system of two interacting tanks in Figure $2,$ derive a second$-$order differential

equation that relates the second tank level $(h_2)$ to the feed flow rate $(F_{in}).$ Calculate the steady state gain

$(K),$ the natural period of oscillation $(),$ and the damping factor $()$ for this system. Is the system

overdamped, critically damped, or underdamped?

Figure $2$