The oscillation of liquid in U tube which has an acceleration

IPhO' 2008

1. The problem statement, all variables and given/known data
The U tube contains the liquid.The length of the liquid in U tube is L. If U tube has an acceleration a in X-axis and we make liquid a small oscillation.Find the period of oscillation.



3. The attempt at a solution

I know the answer is 2[tex]\pi[/tex][tex]\sqrt{\frac{L}{2\sqrt{g²+a²}}}[/tex] but I don't know how to prove it.So,please help me.

IPhO' 2008

g[sup]2[/sup ] is g² and a[sup]2[/sup ] is a².