Non-harmonic Oscillations

Physics

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Non-Harmonic Oscillator

When introducing oscillations at the beginning typically only discuss the harmonic oscillator. This is natural, but this focus may disguise its special features (e.g., frequency amplitude independence). Using the air track, our students investigate oscillations experimentally and match experimental data with theoretical. An additional theoretical choice, along with the damped harmonic oscillator, is the solution for the non-harmonic force law:
 

When there is no damping (=0) there is a difference of less than 0.06 between the non-harmonic and the harmonic oscillator curves if both have unit amplitude and the same frequency and phase. Still, the accuracy of the data allows discrimination between these models. However, the difference shows up most clearly when damping is present since then the period of the non-harmonic oscillator changes with the amplitude and curves that start in phase become out of phase. A simple approximate solution for this damped non harmonic oscillator has been obtained.

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