The oscillation of liquid in U tube which has an acceleration

IPhO' 2008
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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{g<sup>2</sup>+a<sup>2</sup>}}} but I don't know how to prove it.So,please help me.
 
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g2[/sup ] is g2 and a2[/sup ] is a2.
 

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