Solved: A cubic block of side l and mass density per unit volume is floating in a fluid

Chapter 3, Problem 27

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A cubic block of side l and mass density per unit volume is floating in a fluid of mass density0 per unit volume, where 0 > . If the block is slightly depressed and then released,it oscillates in the vertical direction. Assuming that the viscous damping of the fluid andair can be neglected, derive the differential equation of motion and determine the periodof the motion.Hint: Use Archimedes10 principle: an object that is completely or partially submergedin a fluid is acted on by an upward (buoyant) force equal to the weight of the displacedfluid

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