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Accurate Clock Pendulums$
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Robert J. Matthys

Print publication date: 2004

Print ISBN-13: 9780198529712

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198529712.001.0001

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James’ suspension spring equations

James’ suspension spring equations

(p.121) Chapter 16 James’ suspension spring equations
Accurate Clock Pendulums

Robert James Matthys

Oxford University Press

In 1983, K. James published two useful but rather complicated equations whose purpose was to help design the suspension spring. The equations show the effect that different spring lengths, widths, and thicknesses will have on the pendulum. The two equations are quite helpful, as the suspension spring is without doubt the most complicated part of a pendulum, despite its apparent physical simplicity. The first equation calculates the maximum stress in the spring, which occurs at the spring's top end at the maximum angle of swing. The second calculates how much the pendulum will speed up due to the inherent torque exerted by the suspension spring on the pendulum rod. In this chapter, the second equation is used to show that the suspension spring exerts a temperature effect on the pendulum's timing that is roughly as big as the thermal expansion of the pendulum rod. Anywhere from 16% to 84% of a pendulum's total temperature sensitivity is due to the suspension spring, with the actual amount depending on the spring's dimensions, modulus of elasticity, and suspended weight.

Keywords:   suspension spring, pendulum, equations, maximum stress, temperature, thermal expansion, pendulum rod, modulus of elasticity, suspended weight

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