If a liquid is taken in a U-tube, it maintains equal level in both the columns of the tube.
When air is blown in on side B, the liquid may go down upto point D. The displacement of the liquid is given by BD = x. In the second column, the liquid goes up to E and the displacement is CE = x. As the applied force is withdrawn, the liquid level in the second column comes down because of gravity from E to C. But due to inertia, it overshoots the mark C and goes to F (CF = x), whereas the liquid in the other column also goes up by the same distance. Thus, the liquid starts oscillating in both the columns. This motion of the liquid in the U-tube is SHM as explained below.
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Suppose density of the liquid = r
Height of the liquid column in each column = h
Area of cross section of every column = A
Displacement of the liquid = x
Here  ..... (i)
Since g/h = constant, therefore a ∝ x
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Hence the motion of the liquid column in the U-tube is S.H.M.
The time period of oscillation is shown by 
Using equation (i), we get 
This gives the time period of oscillations of the liquid in the U-tube.
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