Consider a rectangular block with a height h and croms-sectional area A floating in a tank of water h h Figure 1: The block partially submerged in water a) Assume that, in equilibrium, half of the volume of the block is submerged. What is the density of the block? b) Now assume that the center of the block is lifted up a beight y yo (with yo < h/2). Draw a free-body diagram, and write an equation for the net force on the block? c) We know from the study of the SHO that a linear restoring force is of the form F=-kr, where z is the displacement from equilibrium and k is the "spring constant". Write the net force from part (b) in the form Fc-ky, where c and k are constants independent of the height y. What is the effective "spring constant" for the block floating in the water? What is the mass of the block? d e) Since there is a restoring force, if were to release the block it would oecillate. What frequency would it. oscillate with? f) Plot the displacement from equilibrium y of the center of the block as a function of time. (Include 3 periods.) g) Write an equation, in the form y(t)- Acos(ut + o), which describes the displacement as a function of time.