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Various linear systems constitute the backbone of introductory physics because they are described by mathematically simple linear differential equations. In particular, the treatment of oscillations in traditional physics courses is restricted, as a rule, to various harmonic oscillatory systems, whose behavior can be almost completely investigated analytically by means of rather simple mathematics accessible for college and undergraduate university students. However, we should realize that such restrictions might lead students to a distorted conception of oscillatory physics as a whole. Detailed investigation of linear systems is certainly very important, but insufficient. The periodically forced linear oscillator (with harmonic potential) gives only periodic motion of the same period in the steady-state response. Specifically, under sinusoidal driving force this steady-state motion is also purely sinusoidal – its spectrum consists of the single (principal) harmonic whose frequency equals the driving frequency. Various anharmonic potentials that correspond to nonlinear restoring forces can lead to a great variety of different modes of transient and steady-state responses, including subharmonic and superharmonic resonances, hysteretic transient and chaotic steady-state behavior. Chaos, which is a type of essentially unpredictable behavior exhibited by a variety nonlinear deterministic systems, has been a subject of intense interest during recent years. In order to observe chaotic behavior, however, the equation of motion must be nonlinear. Numerical simulation becomes then an essential tool to aid understanding of the phenomenon. Simulations provide of course just one way of allowing students to better understand science. However, simulations have special advantages. Simulations can produce images of considerable power that help students remember details in a way which equations cannot. Interactivity is also a powerful argument in favour of simulations. Students quickly become bored if they are just passive consumers of information. They learn better when they need to respond frequently to computer software. At the same time interactive software must be sufficiently structured that users do not lose sight of the educational target. The software package NONLINEAR OSCILLATIONS is intended to aid the learning of physics by means of computation experiments. No knowledge of algorithmic languages is required for its successful use. The software is designed to be a desk-top laboratory which can serve as an electronic training course for individual, interactive work on a computer. With these programs, the students have an opportunity to perform interesting mini-research physics projects on their own. Computer simulations provide very clear and impressively vivid illustrations of various physical phenomena. The screen displays subtle details that usually escape us in direct observation. It is possible to change time scales and to widely vary parameters and other experimental conditions. We can investigate interesting situations which are inaccessible in a real experiment. The graphic representation of experimental results allows us to easily collect and understand large amounts of information.
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Nonlinear Oscillations – a Virtual Lab |