Theory of a nonharmonic oscillator

When introducing oscillations, beginning physics courses typically only discuss the harmonic oscillator. This is natural, but this exclusive focus may disguise its special features (e.g., frequency-amplitude independence). Using an air track, our students investigate oscillations experimentally and match experimental data with theoretical curves. An additional theoretical choice, along with the damped harmonic oscillator, is the solution for the nonharmonic force law F=−F0 sgn(x)−γv. When there is no damping (γ=0) there is a difference of less than 0.06 between the nonharmonic 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 nonharmonic oscillator changes with the amplitude and curves that start in phase become out of phase. A simple approximate solution for this damped nonharmonic oscillator has been obtained.