A semiempirical approach to a viscously damped oscillating sphere

P. ALEXANDER; E. INDELICATO

EUROPEAN JOURNAL OF PHYSICS

Año: 2005 vol. 26 p. 1 - 10

0143-0807

A simple model of damped harmonic motion is usually presented inundergraduate physics textbooks and straightforwardly applied for a varietyof well-known experiments in student laboratories. Results for the decayingvertical oscillation of a sphere attached to the lower end of a spring in containerswith different liquids are analysed here under this standard framework. Someimportant mismatches between observation and theory are found, which areattributed to oversimplifications in the formulation of the drag force. A moreelaborate expression for the latter within a semiempirical approach is thenintroduced and a more appropriate description of the measurements is shown tobe attained. Two coefficients account for experimental corrections, which undercertain conditions permit in addition the calculation of specific fluid quantitiesassociated with the oscillating sphere. Rough relations between viscosity anddamping factor under appropriate limits are derived. The laboratory experiencemay also be used to introduce the concept of a semiempirical model and exhibitits utility in physics.