A tale of a clock

Abstract

A computer model has been constructed of a long case clock standing on aresilient surface, or within a case of impaired shear stiffness, whereby thehead of the clock rocks in response to the swinging of its pendulum. Theequations of motion are written in matrix form, and are solved by matrixinversion. The model accounts for the tendency of such a clock to stop whenits driving weight has descended to about the level of the bob of thependulum. The model predicts that the lengthening of the suspension of theweight by insertion of a link would permit the clock to run on until theweight becomes grounded. It also predicts that use of the chiming weight as aresonant absorber, by hanging it from a tuned suspension of fixed length, notonly allows such a clock to run for the full term of a wind, but improves theconstancy of its rate. The effects of a link, and of the resonant absorber,have been verified experimentally.