U-tube with pistons and spring oscillations · IZhO 2021 #1.1
Physics · mechanics
Problem
Water of mass density ρ=1.00 g/cm³ is poured into a vertical U-shaped tube of small constant cross-section s=8.00 cm², such that the total length of water in both legs is l=50.0 cm. Two pistons are placed into one leg of the tube with the spring of stiffness k=1.00 N/m in between. The pistons are watertight and can slide along the tube without friction. At the initial moment, a weight of mass m=10.0 g is placed on the upper piston. Determine the possible frequencies of small harmonic vibrations of the system near a new equilibrium position. The mass of the pistons and the spring can be neglected, the acceleration of gravity is equal to g=9.80 m/s². Consider water as an ideal incompressible liquid.