An Immersed Spheroidal Pendulum Oscillating Near a Free Surface

摘要

This paper describes the development and execution of a simple experiment designed to exercise the elements of a Lagrangian mechanical system model for the motion of a rigid body near an otherwise calm free surface. The experimental apparatus is a planar pendulum for which the pendulum “bob” is a hollow, prolate spheroid with a 6:1 fineness ratio. The device is used in two configurations: (i) a fully immersed, buoyant configuration for which the stable equilibrium corresponds to floating upright and (ii) a suspended, heavy configuration in which the stable equilibrium corresponds to hanging downward. Experiments in either configuration involve motion that begins from rest away from the equilibrium. Adjusting the water level relative to the equilibrium state modifies the depth-dependent hydrodynamic effects such as added mass and radiative damping.