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| Shift in vibrating resonance with decreasing amplitude. |
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| Circlotron:
--- Quote from: Tomorokoshi on April 11, 2023, 01:53:43 am ---Is it a coiled steel string, a steel wire string, or a nylon string? --- End quote --- Both wound and plain steel wire strings did it. |
| Circlotron:
--- Quote from: twospoons on April 11, 2023, 02:30:55 am --- --- Quote from: Circlotron on April 11, 2023, 01:38:16 am --- If this is the case then, this begs the question - why doesn't an LC tuned circuit behave this way? --- End quote --- If L and/or C are non-linear then this would happen to LC tuned circuits too. e.g inductor core heading towards saturation at peak current. One outcome of this is the oscillation is no-longer purely sinusoidal. --- End quote --- Yes. I have noticed this while trying to measure the inductance of a powdered iron toroid by parallel resonating it with a cap and feeding it with a sine wave in series with a high resistance. Resonant frequency varied from 25kHz to 33kHz depending on amplitude, but with relatively low drive. Didn't noticeably vary from sinusoidal though. May have done if I pumped it hard enough. |
| porter:
I've always wondered about guitar string dynamics. Some heavy duty scholars are doing research. Looking around the internet for a bit I came across this https://www.researchgate.net/publication/263471653_The_plucked_string_An_example_of_non-normal_dynamics That begins with this paragraph |O : The plucked string: an example of non-normal dynamics David Politzer∗ California Institute of Technology, 452-48 Caltech, Pasadena, CA 91125 (Received June 26, 2014; Accepted) Abstract The motion of a single Fourier mode of the plucked string is an example of transient, free decay of linear, coupled, damped oscillators. It shares the rarely discussed features of the generic case, e.g., possessing a complete set of non-orthogonal eigenvectors and no normal modes, but it can be analyzed and solved analytically by hand in an approximation that is appropriate to musical instruments’ plucked strings. |
| ejeffrey:
--- Quote from: Circlotron on April 11, 2023, 01:38:16 am ---Okay. I note that the frequency of oscillation of a pendulum is somewhat amplitude dependent as well, but for different reasons. But physics being what it is, maybe there is a relationship. https://en.wikipedia.org/wiki/Pendulum#Period_of_oscillation --- End quote --- Both are non-linear at large amplitude but it's a different relationship and the opposite sign. --- Quote ---If this is the case then, this begs the question - why doesn't an LC tuned circuit behave this way? --- End quote --- If you use a varactor or an inductor with a core that saturates you will definitely see frequency shift with amplitude. Of course you might design your circuit to minimize this effect, but it's still there. |
| T3sl4co1l:
Indeed if you excite a nonlinear resonator, you'll find a hysteresis loop as it follows resonance as you sweep up (to a point), but jumps through with much less of a peak as you sweep down. Tim |
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