On the critical equilibrium of the spiral spring pendulum

Physical systems such as an inverted pendulum driven by a spiral spring, an unbalanced Euler elastica with a travelling mass, a heavy body with a parabolic section and an Ising ferromagnet are very different. However, they all behave in the same manner close to the critical regime for which nonlinearities are prominent. We demonstrate experimentally, for the first time, an old prediction by Joseph Larmor, which states that a nonlinear oscillator close to its supercritical bifurcation oscillates with a period inversely proportional to its angular amplitude. We perform our experiments with a Holweck-Lejay-like pendulum which was used to measure the gravity field during the twentieth century.