Harmonic Equations Deducible From the Hydrodynamic Motion of a Floating Object

Abstract

Elementary analysis of hydrostatics gives an important result usually called Archimedes principle. Further investigation of this principle in hydrodynamic terms reveal some important properties common to an oscillatory system. The major aim of this paper is to give a brief derivation of a differential equation that best describes the harmonic nature of the motion of an object that is partially submerged in a liquid. The fundamental physical law for a floating object is called Archimedes principle stated as “An object that is partially or wholly submerged in a liquid is acted on by an upward force which equals the weight of the liquid displaced”. However, additional general description of this principle concerning the motion of the object will be established here in an effort to see if the results will be of any particular significance as a problem of hydrodynamics.