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What's the minimum (physics first) to get an oscillator?
nctnico:
--- Quote from: RoGeorge on May 23, 2023, 06:43:26 pm ---That is why asking to identify the essential components of a physical oscillator, at first.
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The way I see it is that in essence you'll need a 'body' that can resonate at a certain fundamental frequency. And then you'll need an energy source that provides energy to excitate the body to resonate at the fundamental frequency or a harmonic. The fundamental frequency is typically determined by how fast waves (electric, acoustic, pressure, etc) can travel through the body and bounce back from the edges.
Even sea waves are a form of oscillation.
IanB:
--- Quote from: RoGeorge on May 23, 2023, 06:43:26 pm ---That is why asking to identify the essential components of a physical oscillator, at first.
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For a harmonic oscillator the essential component is that the mathematical description includes some kind of 2nd order differential equation in time. With a first order system harmonic oscillation cannot happen.
Another kind of oscillator results from switching, for example if you use logic elements to make a square wave. However, if you analyze at a small enough time scale even logic circuits are analog, and somewhere in the description will be 2nd order characteristics.
TimFox:
--- Quote from: westfw on May 23, 2023, 06:25:34 pm ---
--- Quote ---The prototype harmonic oscillator in physics discussions is a spring
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How about a pendulum ? Or does the externality of gravity complicate things?
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My full statement was "The prototype harmonic oscillator in physics discussions is a spring and a mass."
When you analyze the force on the mass (pendulum bob) due to gravity and the constraint of motion with a constant radius, you see a restoring force proportional to the sine of the pendulum angle, which for small amplitudes is extremely close to a force proportional to the angle itself. This gives the same equation as a mass connected to a spring, where the restoring force is proportional to the displacement (and reverses sign with the sign of the displacement).
By the way, when you add "damping" to the simple harmonic oscillator, you need a damping force proportional to the velocity (also reversing with velocity). In a mechanical system, this is conventionally a "dashpot", which is the same basic device used in an automotive shock absorber. Friction does not have the ideal dependences. Such a damping force is analogous to the electrical loss (resistance) in an RLC electrical oscillator.
Nominal Animal:
The only oscillators you cannot describe/approximate (to any desired precision) as some form or combination of (ideal/damped/driven) harmonic oscillator(s) are those based on actual physically discrete states, like certain quantum phenomena. Indeed, one second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 (133Cs).
The duration of many quantum phenomena is surprisingly stable; they're just so darned short they're difficult to investigate.
I'm not exactly sure what RoGeorge meant by numerical oscillators, but all practical use cases I can think of relies on either discrete states or discrete time variable steps, so they're better modeled as periodic systems with either discrete states, or discretely sampled states instead.
For example, in Conway's Game of Life, there are a number of periodic patterns, both static and moving. In many ways, these can be considered time crystals: their base state is not a single state, but a sequence of discrete states, that proceeds without interaction or any transfer of energy.
CatalinaWOW:
--- Quote from: IanB on May 23, 2023, 06:40:03 pm ---
--- Quote from: CatalinaWOW on May 23, 2023, 02:16:42 pm ---The relaxation oscillator highlights the fuzzy line between ideal models and reality. The conceptual oscillator can't be fully described by a differential equation because the trigger circuit is non continuous and has no meaningful derivatives. But it can be approximated mathematically and the physical reality can be matched by those approximations.
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This is an interesting question. What is an "ideal model"? It is presumably a model where simplifications have been made to eliminate some less significant details and make it easier to work with. For example, texts on differential equations nearly always introduce the student to linear differential equations because they often permit an analytical solution to be obtained. But this is an idealization, since the real world is not often linear.
In the real world beyond college and textbooks, complex systems are simulated numerically on a computer, and (possibly gross) nonlinearities in the system can be accommodated.
For example, suppose you put an audio amplifier into a feedback loop by putting the microphone close to the speaker. The amplifier will saturate, the signal will clip like crazy, and the whole thing will be horribly nonlinear. Yet the system is made up of analog components that can be described with differential equations. There is undoubtedly no analytical solution, but a computer simulation if programmed sufficiently accurately could reproduce in a model what the feedback loop does in real life.
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There is a language problem here. Ideal vs idealized. Ideal in the way you used it means best, or optimum or most useful. Which in different situations can mean simplest or most accurate or cheapest to execute. Idealized in the sense I meant is more in the sense of prototypical. An idealized square wave has zero rise time. And can be approximated to any desires accuracy by a series of harmonic oscillators. But never exactly recreated. So technically this square wave isn't the solution of a differential equation. But I am an engineer and the harmonic series are close enough.
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