Wilberforce pendulum – coupled oscillators

The Wilberforce pendulum is an amazing tool to discover coupled oscillations. The quantitative corroboration of how the difference in the squares of the normal modes scales with moment of inertia surprised me. So this can go beyond a classroom demo and become a rich sandbox for studying nonlinear, coupled oscillations.

Wilberforce pendulum harmonic oscillator

The harmonic oscillator, with all its manifestations, is an extensively studied system. It possesses a single degree of freedom. More complicated systems have more degrees of freedom, for example, two pendulums connected by a spring.

In such cases, the behaviour of each variable influences the other which leads to a coupling between the individual degrees of freedom. Energy can toggle between the two degrees of freedom. A well-known example is the Wilberforce pendulum. Hhere the oscillation alternates between the longitudinal stretching of a vertical spring and the rotation of a cylindrical object hung at the end of that spring.

The aim of this experiment is to investigate the dynamics of the Wilberforce pendulum.


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