The Foucault pendulum with an ideal elastic suspension string

Abstract

It is interesting and instructive to compare the precession of a Foucault pendulum, which has an inextensible suspension string, to the precession of an ideal elastic pendulum, for which the string force is proportional to string length (a harmonic oscillator). For the latter case, a simple derivation is presented of the bob trajectories as seen by the local observer on the rotating earth. It is shown that the initial precession rate is equal to the precession rate of the Foucault pendulum, and that the precession period is equal to the rotation period of the earth. The different precession period of the Foucault pendulum may therefore be seen as a cumulative effect of its inextensible suspension string, which constrains the motion of the bob. It is also shown that the initial angular acceleration of the oscillation plane of the ideal elastic pendulum is opposite for opposite initial azimuth angles. If any such difference were observed for a real Foucault pendulum, it might indicate the presence of effects due to elasticity of the suspension string. Another interesting application of the present derivation would be to the precession of the spring-mass oscillator.