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What's the minimum (physics first) to get an oscillator?

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RoGeorge:
So, it's the particular arrangement of a given set of rules, plus the interaction between them, and that makes a certain behavior to emerge.

In the physical world, the set of rules would be the laws of physics.  And to make a particular arrangement out of them, it usually means to put some in close proximity, such that those laws will be interacting with each other.  There's so much to speculate in this direction.

The idea of everything taken as emergent behavior feels like an epiphany, because until now I was considering as emergent phenomena only the appearance of something that it is not really there, for example a bank of fish being "repelled" by a predator.

TimFox:
In physics, the harmonic oscillator in its various forms (simple, damped, forced, coupled, etc.) is fundamental to many other phenomena, and freshman physics concentrates on it accordingly.
Often, analyzing such systems in terms of energy is easier to understand than an analysis in terms of forces, but the physical results are the same.
In advanced classical physics,  the Hamiltonian re-formulation of Newtonian mechanics is a very powerful tool to deal with more complex systems with many degrees of freedom, defining a "generalized co-ordinate" and "generalized momentum" for each degree of freedom (which may not be perpendicular to each other), and later work used the Hamiltonian approach for quantum mechanics.
A good senior-undergraduate textbook for such topics is by Goldstein  https://physicsgg.files.wordpress.com/2014/12/classical_mechanics_goldstein_3ed.pdf
See Chapter 6 for a detailed description of oscillation.
(When I purchased the first edition back in 1969, I believe it cost $17.  Much later, I purchased the third edition for approximately $110.  The above link is a downloadable huge pdf.)

CatalinaWOW:

--- Quote from: RoGeorge on May 27, 2023, 03:22:15 pm ---So, it's the particular arrangement of a given set of rules, plus the interaction between them, and that makes a certain behavior to emerge.

In the physical world, the set of rules would be the laws of physics.  And to make a particular arrangement out of them, it usually means to put some in close proximity, such that those laws will interacting with each other.  There's so much to speculate in this direction.

The idea of everything taken as emergent behavior feels like an epiphany, because until now I was considering as emergent phenomena only the appearance of something that it is not really there, for example a bank of fish being "repelled" by a predator.

--- End quote ---

You are in some deep philosophical ground there.  Newton's laws, the spring constant relationship and other rules are our description of how the system works.  We like the description because it matches behavior.  But I don't think the rules make the system.  The system is, and happens to conform to some degree to a set of rules we have constructed.  We may or may not understand the underlying system.

The most common example to make this point clearer is the use of epicycles to describe the motions of heavenly bodies in a geocentric model of the cosmos.  These rules actually worked quite well, and described the behavior of the visible bodies in the sky to the limits of observational accuracy for millenia.  It wasn't until about 500 years ago when the very detail measurements of Tycho Brahe started to show discrepancies with the simpler epicycle models.  And more complex epicycle models were constructed to explain the new data.   Today most would agree that actual reality doesn't conform to these sets of rules.

The glib answer to your question of why the energy transfers back and forth is because nothing is stopping it.  If you connect a charged capacitor to an inductor what is stopping that charge (and hence the stored energy) from flowing through the inductor?   In this case the inductor puts up a bit of a fight, generating a counter voltage - the back emf - proportional to the change in current.  But it only slows, does not stop the flow.  At some point the voltage on the capacitor drops below the back emf and the sign of the current change reverses.  Now the inductor is pulling charge out of the capacitor to prevent instantaneous magnetic field collapse.  Which continues until the field reaches zero, where it turns out that all of the charge has returned to the capacitor.

Same exact situation as releasing a mass attached to a stretched spring.  Nothing is stopping the mass from moving so the spring has its way.  For a while.

jwet:
Quartz crystals also have this bouncing feature- strain to electricity, electricity to strain.  Its not a necessity of the physics but it does make for an "efficient" oscillator.

TimFox:
An interesting difference between resonators such as quartz crystals and simple oscillators (mass and spring) is that resonators can have multiple resonant frequencies, while simple oscillators have only the one.
One-dimensional resonators (organ pipes, violin strings, resonant transmission lines, etc.) have harmonic overtone frequencies (integer multiples of the lowest or fundamental resonant frequency), but three-dimensional resonators (quartz crystals, resonant cavities, etc.)  have overtones that are not harmonic frequencies.

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