[1] A uniform, vertical U-shaped tube contains water. The total length of the water column is L. (a) When the water column is in equilibrium, the water surfaces in the two arms must be at the same height, of course. If we now shake the tube slightly, the water column will start to oscillate. Prove that the oscillation is simple-harmonic, and find the expression for its period I. Neglect all frictions, and assume that the tube remains in the vertical position at all times. (Hint: How much more weight does one side have when the other side moves down from its equilibrium position by an amount x?) (b) If L = 26 cm, find the frequency f of the oscillation