If the hydrometer is in equilibrium, the weight is balanced by the buoyancy force on it by the fluid. When hydrometer liquid is pressed by x distance the net unbalanced force in the upward direction is given by F=−( Area × Density × Gravity × Distance moved by fluid) Where, -ve sign shows that the direction of force will be opposite to the direction of motion. Thus, m
d2x
dt2
=−πr2ρgx Were, r= radius of liquid column ρ= density of liquid x= distance moved by liquid Now,