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An empty cup made of an unknown material of mass density px, having a cylindrical shape of inner radius r, outer radius R, height L and bottom thickness d, is floating on water (see Figure below). The bottom of the cup is parallel to the water surface and depth h blow. Let the mass density of water pw. gravitational acceleration g, and answer the following questions. 1. Express the mass density px using other quantities. [10pt] 2. If the cup is slightly displaced in the vertical direction, it will undergo harmonic oscillations. Ignore the resistive force and find the period of the oscillations. [10pt] 3. Suppose that resistive force R = -b v, where v is the vertical velocity of the cup, is present. Find b when the cup undergoes critically damped oscillations. [10pt] R h