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Re: [Phys-L] a counterintuition: please examine

interleaved.

On 2021/Jul/19, at 08:51, John Denker via Phys-l <phys-l@mail.phys-l.org> wrote:

On 7/16/21 4:36 PM, bernard cleyet wrote:
If my derivation is correct W/O confounding approximations, adding
mass to a driven pendulum causes a decrease in amplitude.
Horologists have long known that adding mass does not increase the Q,
at least in their experience. More correctly, that is, if I’m
correct, it at least decreases the amplitude, the opposite of what an
increase in Q would cause.


http://cleyet.org/Pendula,%20Horological%20and%20Otherwise/Bob's%20mass%20affects%20driven%20pendulum's%20amplitude_/Amplitude(bob%20mass).1.key.pdf
The question is ill-posed. The situation is underspecified several
times over.

There are lots of ways of "adding mass" to an oscillator, none
of which are simple. This is an "OTBE" problem ("other things
being equal") ... because, as usual, it very much depends on
/which/ other things you imagine to be held equal.


Absolutely every “thing” stays the same except the mass, therefore, it is added in such a way that the frequency does not change.


Here's an unforgettable illustration of how bad OTBE problems
can be:
https://www.av8n.com/physics/causation.htm#fig-multi-fulcrum

1) The least-complex possibility is to add mass
/during the design phase/
and compare to another oscillator without the added mass.
Even then, some OTBE questions remain:
-- Do we imagine constant restoring force (spring), or
constant frequency (pendulum), or what?

both, I thought that was clear from the ODE.

-- Do we imagine the damping depends directly on mass?
(It almost certainly depends on frequency.)


damping does not change. It’s the gamma in the ODE. (freq. no change)

2a) If you try to add mass during operation, it's a huge mess,
because mass is conserved. You have to examine where the
added mass is coming from. Since mass is flowing across the
system boundary, it's nearly certain that momentum and energy
are also.


In my previous post (the second, this is the third) I explained the added mass was done W/the pendulum stopped.

Note: experimentally extremely difficult, however, here are some methods.


1, the support is absolutely rigid (added mass will affect the operation if not rigid)
2, mass may be added by changing the bob’s metal (from brass to tungsten W/the same size, etc.) so dissipation the same.

Note: there is a problem if the result is as I predicted, the dissipation will change W/ the reduced amplitude. Can be compensated by changing the atmosphere causing the dissipation, As I wrote very difficult to do experimentally.

3 and more; I think one will now understand what I’ve attempted.


2b) OTOH if you look at the electrical analog, there are ways
of changing the parameters (L and C). A particularly clear
example is a mechanically variable capacitor:
https://en.wikipedia.org/wiki/Variable_capacitor


I beginning to suspect a pendulum oscillator may not be exactly duplicated by an electrical one.

I don’t see how one can add “mass” in an electrical osc. changing the other element (C or L) to keep the freq. the same, don’t think is the same as W/the pendulum.

Similarly, there exist mechanically variable inductors.

Variable capacitance is easier to understand than variable
mass, but it is still quite complicated. We are now talking
about /parametric oscillators/. They involve some fascinating
physics. They have tremendous practical applications. They
are not nearly as widely familiar as they should be.
https://en.wikipedia.org/wiki/Parametric_oscillator

3) You can define a damping factor that controls loss per unit
time, but Q is loss /per cycle/ so that raises another OTBE
question. Sometimes horologists assume the cycle time is held
constant, but not always. The cycle for a long-case clock is
quite different than a quartz wristwatch.


BTW, A quartz wrist watch is just a high Q tuning fork, not a true quartz clock. The original, IIRC, was a quartz cylinder. The relevant article is in the Bell Tech. Journal next to the Article on microwave optics, which is why I discovered it!

4) Asking about a "decrease in amplitude" is also underspecified.
Much depends on how the oscillator is driven.

The ODE doesn’t care how the pendulum is driven.

In the electrical
case, you can have low-impedance constant-voltage drive, or you
can have high-impedance constant-current drive, or anything in
between. Not to mention the aforementioned parametric drive.

Closely analogous statements apply to mass-on-a-spring oscillators.

*) And so on. Much depends on what the practical objective is.
A child's watch today is almost as accurate as a battleship
captain's chronometer from a couple hundred years ago. That
was not achieved by adding mass.

My exercise was just to note a character of the ODE. Perhaps if the mass increase is very large and the method as mentioned above done, the amplitude change “might” be noticed. I posted to find if anyone agreed in my use of the ODE.

bc .. was about to give up.

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