Motion of an oscillating liquid column in a U-tube is simple harmonic and time period is independent of the density of the liquid. Acceleration of liquid in U-tube is: is directly proportional to the displacement and directed towards the mean position. Hence, the motion is simple harmonic motion. The time period of oscillation is given by: T=2π√(
L
g
).Where L is length of liquid in a U-tube, and the density of liquid is p, and g is acceleration due to gravity. Hence, the time period is independent of the density of liquid.