great interesting problem!!in the limit as one surface area<<the other surface area, I believe its sqrt(g)=w
To get the equation that models this you need to take into account the dampening due to the frictional effects of the pipe. So you need to take into account the head loss of the system.
Yoni: Can't be sqrt(g) - the units don't work out.Aryeh: That will affect the overall equation of motion, but that shouldn't affect the frequency.
I know. I wasn't talking about the frequency, I was talking about the equation to model position, velocity, and acceleration of the system in respect to time.