Motion of an oscillating liquid column in a U-tube is :

The motion of an oscillating liquid column in a U-tube is a classic example of Simple Harmonic Motion (SHM). When the liquid is displaced from its equilibrium position, a restoring force is generated by the weight of the excess liquid column in one arm, which is directly proportional to the displacement. The time period for this oscillation is given by the formula T = 2π√(h/g) or T = 2π√(L/2g), where 'h' is the height of the liquid column and 'L' is the total length of the liquid. Crucially, the derivation shows that the density (ρ) of the liquid cancels out in the equation of motion because both the restoring force and the mass of the liquid column are proportional to density. Therefore, the time period is independent of the liquid's density.