A cylindrical tank with height $8$, radius $2$, and weight $24$ lbs is vertically submerged in water, with y(t) the height of the tank above the water. Two forces act on the tank, the acceleration due to gravity, $32\frac{ft}{s^2}$ acting in the opposite direction of y and the buoyancy force by Archimedes principle.
If water weighs $62.4\frac{lbs}{ft^3}$ then the buoyancy force is
Therefore the differential equation modeling the forces on the tank is $= 0$

Note that weight = force = ma