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What's the minimum (physics first) to get an oscillator?
rstofer:
Attached is a MATLAB/Simulink simulation of a mass-spring-damper. If the D terms goes to 0, it is an oscillator.
The solution is based on the work of Lord Kelvin. Basically, we assume we have y'' (but we don't yet) and integrate it to get y' and then integrate again to get y. Now we sum up the scaled values to create y'' and stuff it back in the input (now that we actually have it). This is the genius of analog computing; integrate until you get rid of the derivatives. Notice the IC=-1 term adjacent to the second integrator. It sets the initial condition to -1.
But, as stated above, you need a second order equation to get oscillation.
thermistor-guy:
--- Quote from: RoGeorge on May 23, 2023, 01:00:33 pm ---As the question say, how to explain an oscillator, and what's the must have for an oscillator?
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--- End quote ---
Oscillation in what domain, exactly?
Predator-prey populations can oscillate.
Many organisms have a sleep-wake cycle, and this is old in evolutionary terms:
https://www.caltech.edu/about/news/surprising-ancient-behavior-jellyfish-79701
There is a long cycle in human affairs. We are currently in the cycle phase called "The Fourth Turning"
https://en.wikipedia.org/wiki/Strauss%E2%80%93Howe_generational_theory
When you say "physics first", I assume you are reaching for something fundamental to all
domains where oscillation occurs. Are you aiming the question at electrical and mechanical
systems only?
Brumby:
My first thought was: Build an amplifier. ;D
IanB:
--- Quote from: CatalinaWOW on May 24, 2023, 01:38:01 am ---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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I was using ideal in exactly the sense you described, to mean idealized or perfect. So I would say that an ideal or perfect square wave model has been simplified to remove such imperfections as finite rise time, or overshoot, that inevitably occur in the real world and that do not need to be considered for many purposes.
IanB:
--- Quote from: thermistor-guy on May 24, 2023, 03:38:17 am ---Oscillation in what domain, exactly?
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It doesn't really matter, due the principle of analogous systems. It turns out that if you construct a mathematical model starting in any given domain, and then reduce it to dimensionless form, you generally end up with the same model to describe the same kind of system behavior.
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