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A U-shaped tube contains some liquid. The liquid column in each half of the tube has length 
, as shown in the figure I below.
The liquid columns are displaced vertically. The liquid then oscillates in the tube. The liquid levels are displaced from the equilibrium positions as shown in figure II above. The acceleration 
of the liquid in the tube is related to the displacement 
by the expression
where 
is the acceleration of free fall.
The length of each liquid column is 
. Determine the period 
of the oscillations.
The oscillations of the liquid in the tube are damped. In any one complete cycle of the oscillations, the amplitude decreases by 
of its value at the beginning of the oscillation. Determine the ratio
.
.
