Experimental study of coupled oscillations on a Slinky Wilberforce pendulum

The Wilberforce pendulum is a mechanical oscillator often used to demonstrate the phenomenon of coupled oscillations. It is a spring-mass system whose pendulum bob contains lateral rods to vary its moment of inertia, being possible to verify the coupling of the rotational and longitudinal motions of the resonant system. In the present work, we present a experimental study of the coupled oscillations on the Wilberforce pendulum using easily accessible materials. With a Slinky spring toy, a wood rod containing masses at the extremities and getting images of the movements using a mirror and the tracker software on a smartphone, we could analyze quantitatively the properties associated with the coupled oscillations. The final result has indicated excellent agreement with the theoretical modeling, and therefore it can be used in teaching of wave physics