Author Topic: What's the minimum (physics first) to get an oscillator?  (Read 9549 times)

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Online bdunham7

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #25 on: May 24, 2023, 04:16:25 am »
Take a Geiger counter and connect the output, with appropriate buffering, to a clock divider circuit like the ones that divide down a 32768Hz crystal oscillator, set up to put out a 1Hz 50% duty cycle square wave.  Now put the Geiger counter in a box along with a gamma-emitter like Cobalt-60 and adjust the sample position until you get approximately a 1Hz output from the divider circuit.

Is that an oscillator?
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Offline IanB

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #26 on: May 24, 2023, 04:21:11 am »
Take a Geiger counter and connect the output, with appropriate buffering, to a clock divider circuit like the ones that divide down a 32768Hz crystal oscillator, set up to put out a 1Hz 50% duty cycle square wave.  Now put the Geiger counter in a box along with a gamma-emitter like Cobalt-60 and adjust the sample position until you get approximately a 1Hz output from the divider circuit.

Is that an oscillator?

Well, that would depend on how you wish to define oscillator.

But in a physics sense, there is no feedback, no momentum effect, no second order dynamic behavior of the process.

It would seem more like a random number generator.
 

Offline RoGeorgeTopic starter

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #27 on: May 24, 2023, 08:20:12 am »
It gets even more bamboozling when thinking about numerical oscillators.
Numerical oscillators?  Do you mean periodic functions and periodic sequences?

Something like that.  That type of question comes from an email "debate".  At some point I was trying to look at the behaviour of a (physical) band-pass filter as a variable impedance, where the energy at the filter input will be reflected back (when the input impedance does not match), or transferred to the output.  Probably a wrong way to look at a filter, it was about switched filters and in another context, anyway,

TL;DR, the other guy asked "if you say a filter is an impedance mismatch reflecting back some input energy, then what is reflected back in a numerical filter, like a DSP?".

I should have stay to physical oscillators only, and not mention the numerical implementations, that's another talk entirely, sorry.

Offline RoGeorgeTopic starter

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #28 on: May 24, 2023, 09:00:24 am »
That is why asking to identify the essential components of a physical oscillator, at first.

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.

For mathematicians, derivatives can mean a lot of things and do many tricks.  To me, less skilled with math, first derivative means the slope of a plot, or speed in mechanics.  And the second derivative means to me the curvature of a plot, like acceleration in mechanics.  I prefer thinking rather in physical terms, like speed and acceleration, because it's something that can be directly experienced by everybody.

So, if I try to translate 2nd derivative in words, would it be correct to say an oscillator needs some sort of acceleration in its behavior?  If yes, then a rotating disk would also be an oscillator.  This might still be OK (saying "might" because just like ejeffrey, I'm tempted to think circular motion is not the same as an oscillator), but the 2nd derivative condition doesn't make any good if, for example, it's a linear acceleration.  Something has to repeat, to be periodic, to alternate.  I don't see how the 2nd derivative implies alternation, or am I misunderstanding the 2nd derivative condition you were mentioning?

To me, the problem of explaining something in terms of math is that there is no causality in an equation.  An equation is an equivalence, a relation between it's terms, and that can only be true or false.  It's like saying an oscillator is something that satisfy the oscillating conditions.  That would be a circular definition, same as saying an oscillator is an oscillator.

I'm not dismissing your explanation, only trying to say what I didn't understood, or what difficulties I have with it.
« Last Edit: May 24, 2023, 09:39:13 am by RoGeorge »
 

Offline T3sl4co1l

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #29 on: May 24, 2023, 10:06:32 am »
Quote
The prototype harmonic oscillator in physics discussions is a spring

How about a pendulum ?  Or does the externality of gravity complicate things?

We could do some interesting categorization with respect to the decay mechanism (or conversely, gain when applicable).  Note that simple rotation decays over time, resulting in a reduced frequency.  That's a very nonlinear sort of behavior compared to SHM.  Depending on the loss mechanism, the decay might be exponential, or double-exponential or something else (compare constant frictional resistance vs. friction proportional to angular velocity*).  Or it might be increasing, with a hyperbolic decay curve -- as for an orbital system (frequency ~ 1/energy) decaying under gravitational radiation.

*Well... there was a kernel of something more interesting in my mind, but it doesn't sound very special when written out, does it?  Simple resistance is torque proportional to angular velocity, which gives a simple pole (exponential decay), the usual case.  But there are mechanisms which are strongly dependent on rotation rate, or frequency (in quantum terms, E ~ ν, but the emission / coupling rate matters too, and I don't know offhand any figures for that), or say temperature (radiation ~ T^4).

Say we stick a magnet or battery to the rotor, so it's emitting EM waves at the rotation frequency; at most frequencies, it will be a short dipole so loss varies strongly with frequency.  (Ah, but does it vary proportionally, or square law, or more?  I don't recall offhand**.)

But these are more easily collected by specifying an amplitude- or rate-dependent function, and observe the special cases for loss = 0 (perpetual) and loss ~ rate (constant resistance), then solve for whatever the resulting decay curve is (or infer the opposite way just as well).

**Well, induced voltage (relative to a non-rotating reference frame) is proportional to rate, and, what, a short dipole has radiation resistance as 1/λ^2?  Which will be the series equivalent resistance of the lossy capacitor, so...
V ~ ω
I ~ V / Xc ~ V ω ~ ω^2
λ ~ 1/ω
R ~ 1 / λ^2 ~ ω^2
P ~ I^2 R
P ~ ω^6 ??


One class is that any convex shape is analogous to a sphere.  (There is a better mathematical term for this, but I can't recall it right now.)

Gaussian curvature..?


Quote
There is a third one, too: the smaller the amplitude compared to the energies and distances involved in an oscillator, the closer it seems to match a harmonic oscillator.  However, I myself do not know why this is, or even if it is just a practical result of a noisy universe (i.e., any non-harmonic components drowned in noise in real life), so I consider it more or less just a rule of thumb.

In general that's just linearization around a point; in this case, a small cycle around phase space.  If the system is continuous, it approximates a SHO orbit.

I suppose for certain dynamic systems, we can employ transformations to convert limit cycles into limit points, and map non-circular trajectories onto unit circles (thus accounting for harmonic distortion).  The existence of such a mapping, on a given system, might suggest its generalized-SHO-ness.


It gets even more bamboozling when thinking about numerical oscillators.  What would mean energy conservation for a numerical oscillator, or momentum, or seeking minimum energy equilibrium, or inertia?  All these are very important and inescapable in a physical oscillator, yet they don't make much sense, and they seem totally arbitrary for a numerical oscillator.

NCOs are abstracted in a different direction: an iterated transformation (discrete-time) on a discrete state vector (i.e. bits in memory).  We could indeed apply some implementation (whether transistors or otherwise), assign an energy or power cost to the states, or transitions therebetween, and model it the same way -- just with a lot of extra steps.

More tantalizing, I suppose, might be applying such maps as above -- suppose we implement an NCO using "lossless" digital logic, at such a clock rate that the loss tangent of the capacitances is sufficiently negligible, and using an LC oscillator (and whatever applicable phase-shift networks) to afford the various clock phases required for operation.  Then we could have a digital description of a continuous oscillating system, which exhibits rather complex behavior (various period-multiplication effects as the counters roll over from time to time) but overall is nonetheless, not just coherent with, but indeed energetically coupled to, our reference oscillator.

The standard implementation today is very much more mundane; since our information-theoretic efficiency is piss (something like ~10^6 times more energy loss per bit transformation), it's basically a class A amplifier: all power dissipation all the time.  And with all that wasted power, it really doesn't matter what happens.  You have the space for a lot of complicated -- but thermodynamically irrelevant -- functions. :)

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Offline IanB

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #30 on: May 24, 2023, 03:20:07 pm »
So, if I try to translate 2nd derivative in words, would it be correct to say an oscillator needs some sort of acceleration in its behavior?
Yes, but more precisely momentum, or transformation of energy between kinetic (relating to movement) and potential (relating to position) forms.

Quote
If yes, then a rotating disk would also be an oscillator.
No, if it is simply rotating freely on a spindle. Yes, if it involves energy transformations between movement and position (a balance wheel in a watch).

Quote
This might still be OK (saying "might" because just like ejeffrey, I'm tempted to think circular motion is not the same as an oscillator), but the 2nd derivative condition doesn't make any good if, for example, it's a linear acceleration.  Something has to repeat, to be periodic, to alternate.  I don't see how the 2nd derivative implies alternation, or am I misunderstanding the 2nd derivative condition you were mentioning?
Yes, the second derivative enables alternation, but does not guarantee it (there can be overdamped systems).

A second order term is needed for oscillation, but not all second order systems will oscillate.

Quote
To me, the problem of explaining something in terms of math is that there is no causality in an equation.  An equation is an equivalence, a relation between it's terms, and that can only be true or false.  It's like saying an oscillator is something that satisfy the oscillating conditions.  That would be a circular definition, same as saying an oscillator is an oscillator.
An equation if properly constructed is a mathematical model of a physical system. It replaces intuition with analysis, and enables predictions to be made about how the physical system will behave. If you write a good model of a system, you can tell if the system will oscillate.
« Last Edit: May 24, 2023, 03:22:20 pm by IanB »
 

Online bdunham7

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #31 on: May 24, 2023, 03:33:52 pm »
Well, that would depend on how you wish to define oscillator.

Perhaps there the terms 'resonate' and 'oscillate' should be contrasted and compared here.  A relaxation oscillator seems to not quite fit some of the definitions of 'oscillator' that I'm seeing discussed here.  The only difference I can see between my proposed device and a relaxation oscillator is that the latter works by the accumulation of physical energy and the former accumulates a record of the energy.  You could redesign things so that each pip of the Geiger counter would add a small charge to a capacitor until a neon bulb discharges it.  Would that be different?

Quote
It would seem more like a random number generator.

If it were a black box, how would you describe it based solely on it's output?
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Offline T3sl4co1l

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #32 on: May 24, 2023, 03:56:49 pm »
Quote
If yes, then a rotating disk would also be an oscillator.
No, if it is simply rotating freely on a spindle. Yes, if it involves energy transformations between movement and position (a balance wheel in a watch).

Why so chauvinistic about kinds of energy transformations? ;D

Free rotation being the exchange of linear kinetic energy between orthogonal axes.  The state variable and conjugate are position and position (or velocity or whatever).  It bears all the other hallmarks, like centripetal force implying energy storage (and indeed storing a little in the material elastically, though usually not enough to worry about).

I understand the feeling though. It seems too trivial or simple a form. :)

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Offline westfw

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #33 on: May 25, 2023, 01:55:17 am »
Quote
a rotating disk would also be an oscillator.
Certainly any point on the disk (except the center) appears to oscillate in nice sinusoids on any one-dimension axis.
I'm not sure how that ties in to the need for energy transfers... 
 

Offline RJSV

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #34 on: May 25, 2023, 02:16:11 am »
Dealing with low level logic,  the essential 'work horse' concept is the simple inverter, allowing for some complexity in the time domain, with certain hookups (or topography).
   So, skipping the complexities of integrals and differentials, is just a few logic gates, and time delays in propagation, AN OSCILLATOR can be had, and can be described, inside a 'paradox' structure.  For the particular paradox, being harnessed, your oscillator needs to be under two rules:
   #1.).   Output follows input logic level, with perhaps optional gain.
and
   "2.).  Input is generated by processing output through an inverter, where both signals are digital, or two state having thresholds for switching requirements.

    I think that's a logic defined oscillator, vs. the analog definitions seen in some replies here.
 

Offline jwet

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #35 on: May 25, 2023, 02:40:04 am »
Okay - here are the definitiive answers* to all these questions-

The radioactive decay example isn't an oscillator.  It is a sensor measuring a random natural process which isn't oscillatory- doesn't repeat and has no period.

Taking a component of rotary motion is an oscillator whether with a crankshaft, cam or balance wheel cogging effect.  A rotating disk alone is not an oscillator.

NCO's are not oscillators- they are summers, they require an oscillator to operate

*- I'm being facetious of course- there are thousands of these kind of stipulated functions that we use every day.  I think its best not to think about them too heavily lest you get sucked into your naval.




 

Online SiliconWizard

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #36 on: May 25, 2023, 03:52:01 am »
To answer "what's the must have for an oscillator?", I think the most basic answer would be: any system that can have at least 2 states, and some energy. One may reply to this that any physical system that can have more than 1 state implies the presence of energy, so that would simplify to just: some energy.
 

Offline thermistor-guy

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #37 on: May 25, 2023, 04:58:41 am »
My first thought was: Build an amplifier.   ;D
Or a switch-mode power supply.
 

Offline T3sl4co1l

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #38 on: May 25, 2023, 08:42:40 am »
To answer "what's the must have for an oscillator?", I think the most basic answer would be: any system that can have at least 2 states, and some energy. One may reply to this that any physical system that can have more than 1 state implies the presence of energy, so that would simplify to just: some energy.

NMR "rings a bell" ;)


My first thought was: Build an amplifier.   ;D
Or a switch-mode power supply.

Class D is still an amplifier for a reason. :D

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Offline RoGeorgeTopic starter

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #39 on: May 25, 2023, 11:15:56 am »
The question originated from an analog oscillator for RF.

Maybe the oscillator's definition should be narrowed down a little:
- physical device
- has an external power source as its only input (any constant DC-like power input, but not necessarily electric power)
- can output a sustained oscillation (of constant amplitude)
- by oscillation, it means a periodic waveform, with a predictable shape and frequency (not chaotic-attractors based oscillator, or alike)
- doesn't need other internal clocks/oscillators

A spring+weight can oscillate, but it's not an oscillator because it's not constant amplitude.  A digital counter, also not an oscillator because would need an external clock, and so on.
« Last Edit: May 25, 2023, 11:20:06 am by RoGeorge »
 

Offline DiTBho

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #40 on: May 25, 2023, 11:21:51 am »


this is as simple, as interesting  :D
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Offline DiTBho

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #41 on: May 25, 2023, 11:31:47 am »
@RoGeorge
I think a good answer comes from the Barkhausen Criterion. It says the principle of the oscillator is that when the feedback factor or the loop gain is one, then the overall gain of the oscillator circuit will be infinite.

So you have blocks, equations in both time and frequency domains, a lot of material, and a criterion!
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Offline IanB

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #42 on: May 25, 2023, 01:28:31 pm »
A spring+weight can oscillate, but it's not an oscillator because it's not constant amplitude.

What about the movement in a mechanical watch or clock? That contains a spring+weight oscillator that has constant amplitude.

External power input is a given for anything that is not a perpetual motion machine.
 

Offline TimFox

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #43 on: May 25, 2023, 03:11:07 pm »
A spring+weight can oscillate, but it's not an oscillator because it's not constant amplitude.

What about the movement in a mechanical watch or clock? That contains a spring+weight oscillator that has constant amplitude.

External power input is a given for anything that is not a perpetual motion machine.

This was supposed to start with physics.
In any freshman physics textbook, discussion of "simple harmonic oscillators" starts with the mass and spring, then we add an external force to get the "forced harmonic oscillator" to understand resonance phenomena, then we add damping to get the "forced damped harmonic oscillator" to understand the frequency response of such an oscillator with explicit energy loss during the oscillation.
The differential equations used in this development then appear in the analysis of analogous oscillators.
In engineering, we then look at "feedback oscillators", where the basic oscillator (e.g., RLC circuit) governs the timing of a packaged circuit to generate a continuous oscillation from an external power source.

 
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Offline jwet

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #44 on: May 25, 2023, 06:28:44 pm »
Barkhausen doesn't cover relaxation oscillators. Make an RC cicuit, connect it to a 100v source, the C will charge up, now, put a neon bulb across the cap, it will trigger at 70v discharging the cap and keep going.  You could make a strained argument that the neon lamp has negative resistance which is gain etc, but this isn't how it operates really.
« Last Edit: May 25, 2023, 06:31:04 pm by jwet »
 

Offline RoGeorgeTopic starter

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #45 on: May 25, 2023, 07:04:04 pm »
I should have wrote self-sustained oscillator, or generator.  An entire mechanical clock is OK as a generator.

Nothing wrong starting with spring+weight, just that those two alone can not produce sustained oscillations.  They will need more component blocks around the spring+weight, so to replace the lost energy such that the amplitude and the frequency remain constant.

I'm tempted to say there are two different mechanisms to keep all in check:
- one is by comparing the amplitude with some reference value, like in an RC oscillator
- the other is by comparing current value with previous value of itself, like in a LC oscillator or alike harmonic osc

Offline T3sl4co1l

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #46 on: May 25, 2023, 07:16:34 pm »
Barkhausen doesn't cover relaxation oscillators. Make an RC cicuit, connect it to a 100v source, the C will charge up, now, put a neon bulb across the cap, it will trigger at 70v discharging the cap and keep going.  You could make a strained argument that the neon lamp has negative resistance which is gain etc, but this isn't how it operates really.

Try it at 100kHz and tell me it's not negative resistance. :)

To put a more subtle point on it -- it can still obey the criteria locally (i.e. for small signals around a turning point), while being nonlinear enough overall to not seem to operate that way ("latches on and off").  Or we can tweak operation towards corners of operation (in this case, at frequencies approaching the deionization time of the plasma) to get a smaller amplitude that more closely approaches the linear conditions we expect for such a system.

Though, keep in mind here too, there is nonlinearity: it may be oscillating, but it's at a low amplitude; what's setting that amplitude?  Presumably there's a negative resistance driving oscillation, but there's a dependent positive resistance that competes, limiting amplitude.

Tim
« Last Edit: May 25, 2023, 07:20:18 pm by T3sl4co1l »
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Offline RoGeorgeTopic starter

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #47 on: May 27, 2023, 08:02:13 am »
Any clues why the energy goes back-and-forth between two forms of storage?  This time asking for the resonator only, without the amplifier or the feedback needed to sustain the oscillations indefinitely.

For example, why the energy changes back and forth between potential and kinetic in a mechanical resonator, or between its electric and magnetic forms in an LC resonator?
« Last Edit: May 27, 2023, 08:05:35 am by RoGeorge »
 

Offline Nominal Animal

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #48 on: May 27, 2023, 01:34:08 pm »
why the energy changes back and forth between potential and kinetic in a mechanical resonator, or between its electric and magnetic forms in an LC resonator?
Because of the structure of the system.

Put snarkily, "If it didn't, it would not be one."

Take a look at potential and kinetic energy in a frictionless 2D pendulum, limiting the angular deflection \$\theta\$ to small angles where \$\sin \theta \approx \theta\$ (small-angle approximation, also simplifies the pendulum to a harmonic oscillator), and assuming all the mass \$m\$ is at distance \$\ell\$ from the pivot point (massless rod between pivot and the tip).  If origin is at equilibrium position, vertical displacement \$h = \ell (1 - \cos \theta)\$, and horizontal displacement \$x = \sin \theta\$, and the pivot point is at \$(0, \ell)\$.  As an isolated frictionless system, total energy is conserved, and therefore the sum of potential and kinetic energy is constant.  You'll find that it is the physical geometry of the pendulum that forces the total energy to swing between potential and kinetic energies, because you can derive the why of the swinging just from the structure, starting from any positive total energy initial point.

For a true simulation of a pendulum, we need to solve the differential equations of motion numerically because no simple algebraic solution exists.  We can do that to any precision we want, and the solutions do converge within all physically sensible initial conditions, even when we model the pendulum itself as a physical object (both continuous matter and "atoms" of interacting particles) in 3D, including the expected difference in oscillation period between the above simplified model (harmonic oscillator) and true pendulum.  So, it is definitely the structure of the pendulum itself that causes the oscillation, not some external principle or cause or rule.
« Last Edit: May 27, 2023, 01:36:42 pm by Nominal Animal »
 

Offline TimFox

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Re: What's the minimum (physics first) to get an oscillator?
« Reply #49 on: May 27, 2023, 01:44:34 pm »
For the spring and mass simple harmonic oscillator (ignoring damping), we start with an initial condition, where the mass is at rest, displaced to position xI away from the equilibrium position x = 0.
Before releasing the mass, all the energy is potential energy of the spring, V = (1/2) k xI2, where k is the spring constant (Hooke's Law) in N/m.
When the mass is released, the "restoring force" F = -k x from the spring will accelerate the mass back towards equilibrium, but when it goes past equilibrium it is moving with a finite velocity and goes past the equilibrium position (x = 0).
At x = 0, there is no potential energy left in the spring:  it has all been converted to kinetic energy of the mass T = (1/2) m v2.
Proceeding past equilibrium, the restoring force decelerates the mass until the velocity and kinetic energy reach 0, and all the energy has been converted back to potential energy in the spring.
We then proceed into the second half of the first cycle, as the mass accelerates back through equilibrium position until it reaches the initial position (no energy loss in this example), stops, and the motion reverses to start the first half of the second cycle.
Etc.
« Last Edit: May 27, 2023, 01:49:05 pm by TimFox »
 


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