The correct cubic relation between the mass configuration of a Kater reversible pendulum and its period oscillation is here described in detail. The geometric study of the complex affine plane cubic curve associated with the period-distance relation allows to conclude that there could be as many as three distinct mass configurations for wich the periods of small oscillations about the two pivot of the pendulum have the same value. We also describe a concrete Kater pendulum realizing this property.
The cubic period-distance relation for the Kater reversibile pendulum
ROSSI, Michele;ZANINETTI, Lorenzo
2005-01-01
Abstract
The correct cubic relation between the mass configuration of a Kater reversible pendulum and its period oscillation is here described in detail. The geometric study of the complex affine plane cubic curve associated with the period-distance relation allows to conclude that there could be as many as three distinct mass configurations for wich the periods of small oscillations about the two pivot of the pendulum have the same value. We also describe a concrete Kater pendulum realizing this property.
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