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Investigation of argumental oscillations of a physical pendulum

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We report an experimental investigation as well as an intuitive theoretical description of argumental oscillations of a physical pendulum, i.e. a driven pendulum where the driving torque depends explicitly on the angle (argument) of the pendulum. With an idealized analysis, we derive three conditions for the occurrence of sustained argumental oscillations: the first establishes the phase matching of the driving system and the pendulum, the second defines the balance of energy gain and loss, and the third identifies the nature of stabilization of the oscillations. For the experimental investigation, we use a recently established pendulum setup, with a further developed suspension mechanism that essentially eliminates friction from the pivot. The pendulum is equipped with a permanent magnet oriented along the pendulum body and a current carrying solenoid located vertically below the pendulum to facilitate an angular dependent excitation. Through studies of free oscillations, we identify the passive electromagnetic pendulum-solenoid interaction as central for the resulting dynamics of the driven pendulum, e.g. it provides a major mechanism of energy dissipation and it modifies the actual dependency of the pendulum frequency on the maximum angle. For one realization of argumental oscillations (Doubochinski's pendulum), we report experimental frequency response curves, i.e. the oscillation amplitude and the phase relative to the external torque as a function of the driving frequency for selected harmonics (n = 5-13) of the pendulum frequency. The results show the characteristic signatures of argumental oscillations derived from the idealized model, but also display clear deviations corresponding to the complex nature of the interaction of the pendulum and the solenoid.

TidsskriftEuropean Journal of Physics
Antal sider28
StatusUdgivet - mar. 2021

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