Finding the period of oscillation of a u-tube w/ water (almost solved)?

[jaron_denson]

Homework Statement

Using the energy method( setting potential energy= kinetic energy) show that the natural period of oscillation of the fluid in a u-tube manometer is t=2PI(l/2g)^(1/2) where L is the length of the fluid column.
2. The attempt at a solution

So as you can see I do not know where the L is coming from, although i just fuged it in when I wrote what wn^2=2g/L. Where is the L coming from? wn^2 should equal coefficents of x divided by coefficents of xprime (aka velocity).

 

[LowlyPion]

You might find this lecture interesting at just about the 21:00 minute mark.