How Does a Fluid Oscillate in a U-Tube with Mercury?

[Bravemeister]

A u tube open at both ends and a uniform cross section contains a mas of mercury,m and a density of 'rho' if the level is slightly disturbed show the surface oscillates with a periodic time of

Tn=2pi sqrt[(m/2g'rho'a)]

where a is the cross sectional area.

i understand how to do this question if it were a spring with a spring constant of k or whatever but i don't know how to do it for a fluid.

I know that circular frequency is sqrt[m/m] and that the frequency is circular frequency/2pi and the time period is 1 over frequency.

the question says the desired result should be found using Newtons laws and the energy method.

 

[NascentOxygen]

You have, of course, tried a google search on "u tube mercury oscillations"?

 

[rude man]

Think about the force of a spring stretched by a distance. Then think of the force on a column of Mercury in a condition of imbalance.