Author Topic: Shift in vibrating resonance with decreasing amplitude.  (Read 986 times)

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Online CirclotronTopic starter

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Shift in vibrating resonance with decreasing amplitude.
« on: April 11, 2023, 12:20:02 am »
Plugged my guitar into one channel of the scope, as you do, and the sig gen into the other channel. Synced to the sig gen and adjusted the pitch of the strings so that the plucked note trace drifted neither to the right or left. What I noticed is that the frequency of the plucked note would initially be dead on, then after maybe half a second it would drift to the right because it's frequency had dropped slightly. Why would this happen? I would have expected it to stay constant.
 

Offline ejeffrey

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #1 on: April 11, 2023, 12:48:05 am »
Because the frequency depends on tension and the tension depends on amplitude.  The larger the amplitude the longer the string and the higher the tension.
 

Online CirclotronTopic starter

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #2 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

If this is the case then, this begs the question - why doesn't an LC tuned circuit behave this way?
 

Offline Tomorokoshi

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #3 on: April 11, 2023, 01:53:43 am »
Is it a coiled steel string, a steel wire string, or a nylon string?
 

Online twospoons

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #4 on: April 11, 2023, 02:30:55 am »

If this is the case then, this begs the question - why doesn't an LC tuned circuit behave this way?

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.

 

Online CirclotronTopic starter

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #5 on: April 11, 2023, 02:32:14 am »
Is it a coiled steel string, a steel wire string, or a nylon string?
Both wound and plain steel wire strings did it.
 

Online CirclotronTopic starter

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #6 on: April 11, 2023, 02:35:33 am »

If this is the case then, this begs the question - why doesn't an LC tuned circuit behave this way?

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.
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.
« Last Edit: April 11, 2023, 02:37:13 am by Circlotron »
 

Offline porter

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #7 on: April 11, 2023, 03:54:42 am »
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.
“It’s all very simple, or else it’s all very complex, or perhaps it’s neither, or both.”
— Ashleigh Brilliant
 

Offline ejeffrey

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #8 on: April 11, 2023, 05:22:47 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

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?

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.
 

Offline T3sl4co1l

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Re: Shift in vibrating resonance with decreasing amplitude.
« Reply #9 on: April 11, 2023, 07:13:15 am »
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
Seven Transistor Labs, LLC
Electronic design, from concept to prototype.
Bringing a project to life?  Send me a message!
 
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