Coupled pendulums sometimes show fascinating phenomena that can amaze laypersons and experts alike. Examples of such pendulums already have been presented in this column.1 Experimental investigations of mechanical oscillations using smartphone apps have also often been described (e.g., Ref. 2). Here, I describe an extension of the experimental possibilities that can be realized by an external sensor box (“satellite box”) in connection with the app Phyphox.3 A suitable application of this satellite box is the direct and simultaneous recording of angular velocity and vertical acceleration in the Wilberforce pendulum.
The Wilberforce pendulum is a great example to demonstrate the conservation of energy. Its movement shows the alternating transition of a vertical oscillation and a rotational oscillation. The theoretical foundations are described in detail in, e.g., Ref. 4. Here, only the motion equations for the two coupled modes of vertical oscillation in the z-direction and rotation...
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