The oscillation of liquid in U tube which has an acceleration

[IPhO' 2008]

Homework Statement

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.

The Attempt at a Solution

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

 

[IPhO' 2008]

g^{2[/sup ] is g2 and a2[/sup ] is a2.}