Classical Dynamics of Particles and Systems · Problem 3-7

Nonlinear Oscillations and Chaos — Marion & Thornton

Physics — Mechanics · oscillations-buoyancy

Problem

A body of uniform cross-sectional area

A = 1

^2

and of mass density

\rho = 0.8

g/cm

^3

floats in a liquid of density

\rho_0 = 1

g/cm

^3

and at equilibrium displaces a volume

V = 0.8

^3

. Show that the period of small oscillations about the equilibrium position is given by

\tau = 2\pi\sqrt{V/gA}

where

g

is the gravitational field strength. Determine the value of

\tau