A pendulum suspended by a flexible beam made of a thin metal strip is commonly used in clocks. However, the usual theory describing its motion is approximate and incomplete. We first recall that simple theory and we then present a more complete theory, which describes the shape of the flexible beam by elasticity theory. We find that the pendulum has two resonant frequencies, corresponding to different shapes of the flexible beam and different motions of the pendulum. The dynamical effects of the flexible beam are directly related to its dimensions and its Young's modulus.
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