科研之友
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摘要
A vibrating stretched string is one of the most fundamental physical systems where non-linear effects play a central role. We describe results obtained with a new, dedicated experimental setup that allows unverified details of the dynamics of this classical problem to be addressed experimentally. The setup uniquely allows simultaneous registration of the transverse motion of the string as well as the longitudinal tension in the string during oscillation over extended times. The explicit non-linear connection between the string tension and the transverse oscillation amplitude is thus directly experimentally determined, allowing us to distinguish between previously reported diverging descriptions. For forced vibrations, frequency response curves for the transverse amplitudes are obtained, and found to be in good agreement with predictions from a simplified model, while the model only qualitatively reproduces the observed phases of transverse oscillation relative to the phase of the driving force. A frequency analysis of the observed string tension reveals a richer dynamics than anticipated from a simple model, and from the observed frequency response curves alone. For free oscillations, the setup is used to demonstrate the variation of the normal mode frequency with the transverse amplitudes. The reported setup is well-suited as a demonstration experiment on non-linear oscillatory phenomena, as well as a student project in either introductory or advanced mechanics teaching.
- 出版日期2017-7
