JoNo’s Pendulum

[Joseph Noci 1Participant @josephnoci1]

Posted by SillyOldDuffer on 03/10/2023 18:46:34:

I've noticed 'twang' too. Likely it occurs in all pendula, but isn't noticed unless the apparatus can measure period at high-resolution.

……

I think the most likely cause of 'twang' is the rod flexing. An impulse applied at the top travels down a long lever to move the bob, which has inertia. The rod must bend, and I'd expect it to oscillate. Moving through air must also vibrate it slightly. Not much, but detectably.

If the rod was a violin string, what frequencies would it vibrate at? (Violin notes are far from pure – they twang too.)

Dave

From Michael:

The two lowest frequencies of a pendulum rod must surely [?] be its first bending mode and its first torsional mode … everything else, I posit, will have a higher frequency.

The magnitude and frequency of both of these will depend upon the construction details of Jo’s pendulum [and they should be simple for him to measure] … but I would expect both to be many octaves above the frequencies he is observing.

I believe I am with Michael on this one –

The rod is stiff and stretched, Its natural resonant frequency would be in the 10s of Hz – I can hear it when I Twang it…Standing waves would only result in higher frequency modes and I am measuring 25 second periods and up…It definitely is not the rod 'vibration' or flexing due to the drive coil.

But I believe I have a Eureka – I am not going to post the chapter, but chapter 15, page 106 onwards, titled 'Energy Coupling between Modes of Oscillation" in Matthys book, Accurate Clock Pendulums is I think definitive of my observation.

In essence , the three oscillation modes are left-right , front-back, and rotation about the rod axis. In his book, a test is done where the pivot is displaced 4deg from perpendicular to the front-back axis, which imparts a strong front-back drive during the left-right motion. That resulting front-back motion ( very small movement..) presented a 6minute period ( mine was 50sec..) where it reduces to 0 and then builds to a max, and repeats – this then couples into the amplitude of the left-right motion, which is exactly what I observe. The pendulum RATE remains largely unaffected , but its time keep is – it runs slower- also exactly what I have observed.

I may also suffer from a rotational rate as well – the front-back and left-right simultaneous motion describes an ellipse to some extent, and can induce a rotational mode as well – a ball or cylinder shaped bob will resist rotational motion to some extent, while my rugby ball bob has more inertial mass out on a limb to perhaps aid that mode's persistence.

It is difficult to detect these phenomena from timing data derived purely from the opto-sensor used at BDC by most folk – These modes are easily induced by the slightest of casual pivot implementations it seems – spring pivot with non-identical spring-pair behavior ( spring clamp or soldering stresses..), pivot centering in the plane of swing, etc….

The opto method does not give amplitude measurement, and although it can be derived from the data, it is not accurate enough I believe.

The clock rate is not affected by induced front-back motion, but as indicated, its time is – Matthys 4deg pivot bias test resulted in a pendulum running 0.68sec/day slower, but stable.

Edited By Joseph Noci 1 on 03/10/2023 21:26:39

[Joseph Noci 1Participant @josephnoci1]

Posted by S K on 03/10/2023 20:00:08:

Interesting stuff. One point: "And solid carbon rods temp coef is a lot poorer than a tube…"

I'm wondering why this should be? Thanks.

Unfortunately, the solid has a vast amount more resin than the thin walled tube, and its the resin that has the poor Tc..

[Joseph Noci 1Participant @josephnoci1]

Posted by Michael Gilligan on 03/10/2023 12:13:12:

 

That is VERY interesting Jo, but I honestly can’t imagine any single vibration mode of your pendulum which could have that [those] period[s] … I therefore suspect that you are seeing a ‘beat frequency’ between two other modes.

How the devil to identify them is way beyond my ability.

MichaelG.

 

Michael, with or without knowing it, you are EXACTLY correct!

Edited By Joseph Noci 1 on 03/10/2023 21:30:27

[SillyOldDufferModerator @sillyoldduffer]

Posted by Joseph Noci 1 on 03/10/2023 21:17:55:

Posted by S K on 03/10/2023 20:00:08:

Interesting stuff. One point: "And solid carbon rods temp coef is a lot poorer than a tube…"

I'm wondering why this should be? Thanks.

Unfortunately, the solid has a vast amount more resin than the thin walled tube, and its the resin that has the poor Tc..

The carbon-fibre rod I used had very good temperature performance even though it reacted strongly to humidity. My guess is the longitudinal carbon fibres fix the length, and it doesn't change much with temperature. However, the flexibility of the rod depends on the resin, which is sensitive to humidity. My rod was very thin and being used as a suspension spring with a lightweight bob, which likely exacerbated the humidity problem. Now I'm using a conventional pendulum, humidity has no effect, but temperature matters.

Dave

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