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

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RoGeorge:
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

T3sl4co1l:

--- Quote from: jwet 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.

--- End quote ---

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

RoGeorge:
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?

Nominal Animal:

--- Quote from: RoGeorge on May 27, 2023, 08:02:13 am ---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?
--- End quote ---
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.

TimFox:
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.

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