Foucault's Pendulum Recreation for Physics Project

[Brad Meacham]

(I apologise if this is the wrong area to post)
Hello everybody

I am planning on building my first Focault Pendulum(As a physics projject for school) and I have a few questions. I am going to purchase a cable(it needs to be smooth and friction-less around 7 feet), I also am going to need to purchase a bob (around 2-3lbs). Now my first question is where can i buy these items? Online has only a few varieties and I do not like my options.

Also what would be the best way to suspend this cable from my ceiling in order to have it rotate 360 degrees without friction causing it to slow?

I was also thinking of purchasing a donut magnet and installing it at the top as a kicker (possibly with an iron collar); if there is too much friction/wind resistance and my pendulum would stop after 2 hours.

Any help, advice, questions, are all appreciated thank you very much for taking the time!

Brad

 

[Vanadium 50]

Also what would be the best way to suspend this cable from my ceiling in order to have it rotate 360 degrees without friction causing it to slow?

And that is the key question in your project.

 

[Andy Resnick]

I am planning on building my first Focault Pendulum(As a physics projject for school) and I have a few questions.

This is not a small-scale project, it requires careful attention to a lot of details. Here's a document with some specifics :

http://www.astro.louisville.edu/foucault/pendulum.pdf

 

[Brad Meacham]

I am not trying to go crazy I figure I would need a massless suspension/aircraft cable, a frictionless pivot, and a hollow bob. I am going to head over to the engineering lab next week so that I can work out some numbers. Is there a website online I can order from? or possibly a place around Portland, Or? Thanks!

 

[Nidum]

Google Images 'Plumb bob' and 'Plumb line' .

You can buy many varieties cheaply in tool stores and online .

 

[Andy Resnick]

I am not trying to go crazy I figure I would need a massless suspension/aircraft cable, a frictionless pivot, and a hollow bob. I am going to head over to the engineering lab next week so that I can work out some numbers. Is there a website online I can order from? or possibly a place around Portland, Or? Thanks!

If you find a source for massless cables and frictionless pivots, let me know- I would be interested in having some of those as well.

 

[jbriggs444]

If you find a source for massless cables and frictionless pivots, let me know- I would be interested in having some of those as well.

https://missionbelt.com/products/unobtainium (tongue deeply embedded in cheek)

 

[Brad Meacham]

what would you suggest I use as alternative materials?

 

[Brad Meacham]

http://www.e-rigging.com/cable
https://www.amazon.com/dp/B0009WG4U4/?tag=pfamazon01-20

How does this cable and plum look? I am working on finding a frictionless swivel they are tough to locate.

Thank you!
Brad

 

[Tom.G]

frictionless swivel they are tough to locate.

Closest I can come up with is a bar balanced on a knife edge, or a ball held up with a stream of air (but that tends to be unstable).

need a massless suspension/aircraft cable

Kevlar fiber (or thread). Light weight, super strong, a little hard to find, used in bulletproof vests.

 

[Brad Meacham]

Does anyone have a recommendation for another bob? or what about a swivel that works pretty well it does not have to be perfect.

 

[Tom.G]

http://www.e-rigging.com/cable
https://www.amazon.com/Johnson-Leve...i&ie=UTF8&qid=1477718638&sr=1-18&keywords=bob

How does this cable and plum look? I am working on finding a frictionless swivel they are tough to locate.

If you want a stiff cable that stuff should fill the bill. You may not be able to straighten it out though.

I think you need a much heavier weight so it has much more kinetic energy; air resistance you know.

 

[Brad Meacham]

What should I type into google to find a heavy spherical symmetrical weight I have tried every combo of words. I found this plumbob 32oz by luck...
Tom your information is incredible I know how to straighten cable so I was thinking of doing this:

get a large ball bearing, ideally plastic or unhardened (or at least not through hardened) steel and then drill and tap it for an attachment point for the pendulum. Then mount this plate with a hole or something like 95% of the diameter of the bearing, for this slip on pipe flanges are convenient. To get the best possible bearing surface I can lap the ball into the join with valve grinding paste or similar. This is a really advanced version, looks doable:

 

[John Mi]

Hi Brad, interested to hear how you went? Especially in how you implemented the 'kicker'.

 

[lesaid]

Hi Brad, interested to hear how you went? Especially in how you implemented the 'kicker'.

Hi - was interested too. I am attempting to develop a 'small' Foucault pendulum of my own - just for the challenge since everywhere says it can't be done on a small scale! For pivot - I am trying a device shaped like a question mark, pivoting on a point at the end of the 'hook', and a rigid pendulum (about 1.3 metres) attached to the downward shaft.

The kicker is a shallow, cylindrical electrode centred under the bob with about 10 kV from a high impedance power supply on it. Each time the bob passes (with a clearance of about 2 mm), a spark jumps which puts a charge on the bob and (briefly) repels the bob from the electrode until the charge dissipates. On the return swing, there is less charge left until the next spark. Amplitude of swing is about 1 cm either side of centre (easy to get larger amplitudes by increasing the voltage somewhat, but I think lower swing angles should be more accurate).

Bob is a clock weight, about 1.5 kg.

Running tests on it now (literally) - gradually finding preferred directions of swing and removing the causes.

Difficult to read angle of swing with any precision with this design - if it proves to work (precess as it should), then I'll think about reading angles more easily! Until then, I take video clips of the swing and can work out the behaviour from those after the experiment is done.

Might give you (or other experimenters in this) a couple of ideas. Interested in anyone with ideas to improve my design too.

 

[Vanadium 50]

Aren't your electrodes rotating with the earth? As you describe it, it sounds like you won't see the rotation of the plane of motion because it's effectively constrained.

 

[lesaid]

Aren't your electrodes rotating with the earth? As you describe it, it sounds like you won't see the rotation of the plane of motion because it's effectively constrained.

I don't think it should. I only have one electrode, which is cylindrically symmetrical, directly underneath the dead-centre of the swing - i.e. where the bob rests when it isn't swinging. The bob also is cylindrically symmetrical. So the impulse given by the electrode, random variability excepting, should be strictly radial, with no tangential component at all. So I think it 'shouldn't' (in a perfect world) have any effect at all on the direction of swing. What I'm trying to do now, as I adjust things, is get the world sufficiently 'perfect' that the rotation of the Earth is the dominant factor affecting the direction of swing.

 

[jfmcghee]

Not sure if you've seen this webpage: http://www3.sympatico.ca/surfin.dude/creative/clocks/foucault/foucault.html
His project is unfinished, but there are some ideas there. Among the links in the page is an old paper for the design of a desktop version. Still a dream of mine to build one for my classroom. Another drop in the bucket of dreams for classroom demos...

 

[lesaid]

Interesting links!

My pendulum is progressing slowly as I identify perturbing influences and modify the design to reduce them sufficiently. Some surprises along the way, and some mathematical challenges to understand the behaviour. I'm trying to do this in the simplest possible way with no electronics (other than a 10 kV power supply), no build techniques more sophisticated than hacksawing brass and soldering brass pieces together with a miniature blowtorch, and mostly made with what I've got lying around. Not, I'm afraid, a prototype for a classroom - more a 'home project' for fun, and hopefully, to prove that a small Foucault pendulum can be built by the ordinary DIY-er. But I guess, if it works, a free-standing desktop version could be developed.

Currently building a simulation model of the design to try to reproduce the behaviour I'm observing, and figure just how precisely my design needs to be built in order to be able to complete a full 24 hour rotation convincingly. So far, it has always settled to a preferred direction, or has oscillated between two perpendicular swing directions - but the period of that oscillation is reassuringly long - something like 90 minutes and I think I've identified a couple of reasons for it which I'm addressing now (very slightly different moments of inertia in different directions, and possible slight flexing of the support for the pivot in one direction).

I have some mathematical challenges with it too, as I try to model the behaviour analytically rather than by simulation.

Might be interesting to discuss this more if anyone is interested - in which case a new thread might be better than hijacking this one!

 

[lesaid]

Among the links in the page is an old paper for the design of a desktop version. Still a dream of mine to build one for my classroom. Another drop in the bucket of dreams for classroom demos...

You don't need such a sophisticated setup for a desktop Foucault pendulum. While I haven't sorted out the drive properly in mine, it now works as a free-swinging pendulum, and will show up to six hours (just) of precession, at as near as I can judge by eye on a marked piece of card, exactly the rate expected for my latitude. It has a 1.2 metre rigid shaft, a 1.4 kg bob and the pendulum sits on a point, supported by a small platform. The point is tipped by a 1 mm diameter ruby probe on a piece of glazed dinner plate as a hard platform. The pivot support structure is made partly out of wood, and partly out of pieces of brass bar soldered together.

Could build it in a day, given the materials - much simpler than the link that you posted.

I'm now working on quantifying the accuracy of the precession, and on the drive to get it to keep going indefinitely rather than just for a few hours.

Might be a viable project for your classroom. It needs great care to keep the moment of inertia independent of swing angle, and to have a rigid pivot support that cannot be significantly moved or twisted (even by a few microns) by lateral forces from the pendulum. Then it works! My test for these criteria is to start the swing in a circle. If the swing doesn't stay circular as it decays, then the system isn't symmetrical enough.

By the way - I start the swing off simply by releasing it from my fingers - not by burning threads. I'm struggling to understand why most people seem to find unwanted lateral movement such a problem. It is true that in the last stages of the swing decay, the swing becomes circular, but by that time the swing amplitude is maybe 5% of what it started with - not a problem in practice.

 

[sophiecentaur]

I am working on finding a frictionless swivel

I think a frictionless swivel may not be necessary. If the bob itself rotates with the Earth then will that matter, as long as the wire can deflect in different directions? Wouldn't any precession force be working along the direction of the wire, making it irrelevant?
But a swivel with no end stop wouldn't be necessary as the rotation is only 360° in a day. A Hook in a cup* would allow nearly 360° of movement and act as a bearing for the pendulum at the same time. and two in tandem would be even better. You can rotate the mass to the end stop at the start of the exercise.
* A jewelled point in a ceramic cup, for instance.

Another drop in the bucket of dreams for classroom demos...

Been there!

 

[Nidum]

An energiser for a foucault's pendulum can be made using a very small area electro magnet located vertical axis just below and on centre line of pendulum and a system of photo cell detectors .

As the bob comes very near but not actually to the vertical the solenoid is energised for a very short time . This in a minute way pulls the pendulum towards centre without changing it's direction of travel . This tiny impetus repeated each swing or better as necessary when swing of pendulum goes below a set value will maintain swing indefinitely and within practical limits not interfere with the natural action of the pendulum .

 

[lesaid]

I think a frictionless swivel may not be necessary. If the bob itself rotates with the Earth then will that matter, as long as the wire can deflect in different directions? Wouldn't any precession force be working along the direction of the wire, making it irrelevant?
But a swivel with no end stop wouldn't be necessary as the rotation is only 360° in a day. A Hook in a cup* would allow nearly 360° of movement and act as a bearing for the pendulum at the same time. and two in tandem would be even better. You can rotate the mass to the end stop at the start of the exercise.
* A jewelled point in a ceramic cup, for instance.

Been there!

I have found in practice, that a 'hook in a cup' doesn't work, at least, not when made out of thin brass bar. The difference in moment of inertia in the plane of the hook and perpendicular to it was enough to cause the pendulum to trace a lissajous figure, with a cycle time of 60 - 90 minutes, overwhelming the Earth's rotation. Perhaps if the hook were made of a really lightweight material? Or if the pendulum was longer and heavier in relation to the pivot piece (mine is only 1.2 metres long and 1.4 kg).

My solution was to make a 'cage' - think of the 'hook' as being a rectangular 'C' piece, with a downward pointing support from the top, and the pendulum hanging underneath. Now have three 'C' pieces, open ends joined, at 120 degree angles. That has a moment of inertia independent of swing direction (by my calculation) and was necessary to get the pendulum working. The rotation of the cage turned out not to be a problem - it didn't rotate (though it can turn very freely indeed). The swing can go any way without causing the cage to rotate at all. Presumably in an absolutely frictionless pivot, it would rotate too - but my pivot cannot be 'that' frictionless! (a ruby on a piece of glazed china).

The other crucial thing, was a very rigid support bar - even a tiny flex leads to lissajous patterns!

 

[sophiecentaur]

even a tiny flex leads to lissajous patterns!

Oh yes!
Problem with a small scale version is there are so many more significant factors. Nothing like a cathedral dome to get the job done properly. I was contemplating using the stair well of a 4 storey school building but none of my students at the time fancied it as an A level investigation.

 

[sophiecentaur]

The rotation of the cage turned out not to be a problem - it didn't rotate (though it can turn very freely indeed)

Interesting but the time constant (LR?) involved could be many days so it wouldn't matter if there were no swivel, I think.
Edit: I think that may be rubbish or irrelevant but rotation of the ball won't affect the pendulum motion; more important is the symmetry of the suspension, as you imply.

 

[lesaid]

Interesting but the time constant (LR?) involved could be many days so it wouldn't matter if there were no swivel, I think.
Edit: I think that may be rubbish or irrelevant but rotation of the ball won't affect the pendulum motion; more important is the symmetry of the suspension, as you imply.

yes - I measured the flex in the support bar, and found it had a spring constant of something like 5600 Newtons per metre (measured with a x400 USB microscope photographing the end of the bar while hanging small weights off it). Worked out that at maximum swing amplitude (3 cm), the pivot would flex sideways by something like 30-40 microns or so. After stiffening the bar, the problem disappeared.

Now its the driver I'm working on - swinging freely, it takes over six hours to decay too much to measure, so easy to observe the correct rotation. But I would like it to run indefinitely. Thinking electrostatics rather than electromagnets, but getting bogged down in the mathematics as I try to figure out equations of motion resulting from a driver that is slightly off centre. I think it might be beyond my current ability. Might need a computer simulation instead.

 

[sophiecentaur]

For a driver, perhaps consider a loud speaker style electromagnet (coaxial poles) right under the mid position. It would need a circular detector (optical?) to turn on the current briefly as the bob approaches the center. Sensing and driving would be symmetrical.
Just another way of skinning the cat.

 

[lesaid]

= This in a minute way pulls the pendulum towards centre without changing it's direction of travel ..

Is there any advantage in a brief pull towards the centre over a brief push away from the centre as the pendulum passes? Not sure why there should be - my driver pushes rather than pulls, though the driver at present upsets the behaviour of the pendulum in a way that I don't yet quite understand.

Trying to figure out how accurately aligned the driver needs to be on dead centre - and finding the maths challenging!

Wondering whether a pull-push arrangement might be more effective. A pull switching to a push as the pendulum passes overhead, might do a better job of cancelling out the effects of an offset in the driver position. But so far, that is speculation only - I'm trying to figure out if it is true or not! Experimentally, I'm getting conflicting results at the moment.

 

[sophiecentaur]

A pull switching to a push

To achieve a 'push' you would need a permanent magnet on the bob with a very symmetrical field. That is an added complication. Otoh, a coaxially built electromagnet would be fairly easy to make with steel parts (pipe and rod etc) and would Pull a steel bob.

 

[lesaid]

My 'push' is coming from electrostatic repulsion. I have a small domed electrode facing down on a 'stalk' under the bob, and a matching one on a stalk pointing up from below. As the bob passes, a spark jumps which charges the bob - it is then repelled briefly. The charge dissipates through a resistor (60 Gigohm) to ground (via a 50 gauge wire attached at the pivot point just above the ruby) so that by the time the bob swings back, it no longer repels, and is ready for the next spark. Running it at a low voltage with small electrodes ensures the spark happens as close to dead centre as possible.

The pendulum will run at a comfortable amplitude between 5 and 10 kV depending on the spark gap. I chose this approach (a) because I happened to have a controllable EHT PSU, (b) it didn't require any additional electronics or sensing, and (c) I wanted to explore a different approach just for fun. As a driver, it works fine. However, I haven't got it fine tuned enough as it does disturb the swing in an odd way that I'm trying to figure out.

I was also wary about having anything ferrous in the pendulum as there are some strong magnets around here - I didn't want to have to worry about that as a stray influence given the sensitivity of this system!

 

[sophiecentaur]

Bilmey O'Reilly - you are contemplating 10kV for a classroom demo. Have you got a written Risk Assessment and a section about the safety rail / locked room when you are not there?
I get your problem about stray magnetic fields though.

 

[lesaid]

Bilmey O'Reilly - you are contemplating 10kV for a classroom demo. Have you got a written Risk Assessment and a section about the safety rail / locked room when you are not there?
I get your problem about stray magnetic fields though.

actually - I think I suggested using the pendulum free-swinging without a driver for the demo in my first post on this! A six hour useable swing time gives plenty of opportunities to measure the rotation. Though the supply only needs to provide a few tens of nA with a very small capacitance. Do secondary school physics classes not have access to safely current limited supplies of a few kV?

thankfully though - I'm not a teacher - I'm a hobbyist so I don't have to worry about written risk assessments! (been there, done that, in other contexts!).

I was wondering - your A-level students don't find Foucault pendula interesting? I'm curious - what kind of projects do they favour? electronics and robots?

 

[sophiecentaur]

I was wondering - your A-level students don't find Foucault pendula interesting?

That's ancient history now. They seemed most interested in the so called Cosmology bit of the course, mainly and there was not a lot of practical work for that - except for estimating distances out on the school field. Distance from the science block in Parsecs etc.. (Suitably scaled)
On the safety front, the High voltage supply was perfectly 'safe' but I had one lad who got a small belt off the supply and he made a real fuss about it.

 

[lesaid]

On the safety front, the High voltage supply was perfectly 'safe' but I had one lad who got a small belt off the supply and he made a real fuss about it.

Actually - from what I know now about the tiny impulses necessary, I should think that a reasonably strong electromagnet and a few iron filings at the bottom of the bob might be enough - and not enough to be affected much by more distant magnets! If fraction of a second of repulsion between two 4 mm diameter domed bolts at 5 kV is enough to get a good swing - it won't take many iron filings with a decent magnet!

But this way seems simpler, if I can get it to work symmetrically!

 

[sophiecentaur]

But this way seems simpler, if I can get it to work symmetrically!

I would think that an electromagnet with a carefully wound coaxial arrangement could be arranged to be vertically below the top fixing. Your 'few iron filings' could do the trick. You could investigate the actual effect of your weird fields by comparing two bobs - one ferrous and one non-ferrous. (perhaps you've done this already; you seem to have done quite a lot of prep work on this.)
The project sounds serious fun.

 

[lesaid]

It is indeed serious fun - though is about to slow down! I am a 'mature student' working for a mathematics and physics degree - and started this at the beginning of the summer break as a means of doing some 'lab work' at home - and exercise some of the mechanics skills I'm supposed to have been learning! However, the new term is about to begin so I'm going to have to go back to 'proper study' and this will take a back seat for a bit. But will keep going with it at a slower pace. I started with a weight dangling off some string tied to a hook, and have been identifying and fixing the problems one by one. I never expected to get it to work, since I could not find any references to anyone successfully making a Foucault pendulum this small, even with a complex driver. So yes - it's been and still is, exciting!

I'm going to give the electrostatic driver a serious go before I move to magnets. I suspect one problem might be that the discharge wire might have been in contact with a wooden support piece, through which it could have transferred charge to the pivot arm. The wood has a lower resistance than my discharge resistor. Then I'd be getting repulsion between the support bar and parts of the pivot, which might be significant. That would also explain why the charge is dissipating faster than I intended.

On magnets - to make a very symmetrical magnetic field, I think I'd be tempted to place the coil at one end of a long core - so the coil is well away from the 'point of action'. Then, I think, it would be the symmetry of a few inches of protruding core that would matter - and the precision of the coil itself or its mounting shouldn't be so important.

I'm also curious - given how delicately sensitive this is - whether changes in barometric pressure and the effect on air density and drag, might have a measurable effect on the decay rate. But that is something for later!

 

[Tom.G]

might have been in contact with a wooden support piece

given how delicately sensitive this is - whether changes in barometric pressure

Unless it's in a controlled environment, I would be more worried about wood dimensional changes with humidity.

There is a large Foucault Pendulum in Los Angeles at the Griffith Observatory (open 6 days a week).
One thing mentioned is that the top support bearing does not rotate as the building rotates with the Earth. Another is that the drive is a ring magnet at the top.
It has been decades since I visited there, but at the time the staff was quite willing to engage in technical conversations.

Here is a search link:
https://www.google.com/search?source=hp&q=foucault+pendulum+at+griffith+observatory

Observatory website:
http://griffithobservatory.org/

 

[lesaid]

Unless it's in a controlled environment, I would be more worried about wood dimensional changes with humidity.

Yes - an earlier iteration of this design had the entire pivot support made of wood. In order to get the precise control of the pivot platform that I needed, I had to move to brass. The wooden portion provides a frame, attached to the ceiling of the room, to mount things on, and to provide screw adjustments to level things. The load on it is counterbalanced so there is no twisting force on it. So far, it seems to be OK, at least for runs up to six hours at a time. But I don't know how it will behave in the long term, once the diver allows continuous operation!

My comment about humidity was one of curiosity - I've no reason to suspect that humidity is causing a problem!

Actually - if the wood does change size, the effect would be a slight lateral movement of the pivot, unrelated to the swing. What worries me more in this regard is traveling of the pivot point across the platform over time, though this too hasn't shown itself as a problem so long as the swing amplitude isn't allowed to get too high and the platform is kept reasonably level.

One thing mentioned is that the top support bearing does not rotate as the building rotates with the Earth.

Interesting!

It seems to me that the support bearing 'should' stay aligned with the swing rather than the building. But this is not what I observe in practice. My assumption is that the tiny amount of friction between the ruby and the platform is enough to hold the pivot assembly aligned to the platform, and that if my bearing was frictionless enough, it would indeed rotate. Perhaps this is a consequence of scale - mine being tiny by comparison to the observatory. Thankfully the swing direction doesn't seem to be linked to the orientation of the pivot assembly, so this doesn't appear to cause problems.

Actually, given that the pendulum swing shouldn't, as I understand it, exert any torque on the bearing around its vertical axis, if the bearing were frictionless enough that the pivot orientation did rotate with respect to the building, why wouldn't it also rotate if the pendulum was not swinging? In which case, why bother with the pendulum? Not sure how the mechanics works here?

 

[sophiecentaur]

One thing mentioned is that the top support bearing does not rotate as the building rotates with the Earth.

That implies a (sidereal?) clock mechanism, driving the bearing round. So someone must have thought that to important enough to actually implement it.

I'd be tempted to place the coil at one end of a long core - so the coil is well away from the 'point of action'.

Considering the Magnetic Circuit, the position of the coil may not be too relevant as the susceptance of the bar would produce a Pole, pretty near the top end, wherever the coil is placed. The field emerging from the top would (or could) be distorted by nearby ferrous objects (steel framed building, for instance) and that could shift the magnetic centre. My point of using a circular pole round the centre pole was that the field geometry would be very well defined - and also, of course, it would be a lot higher (a la horseshoe magnet) across the gap than would a field from a single ended (bar) magnet. The external field wouldn't matter much because the current wouldn't be flowing. But mine is a hand waving argument and I have no quantitative ideas about the problem - if it actually is a problem. I wonder if a servo, adjusting the position of the driver so that the crossing of the bob is kept vertically below the pivot.

 

[lesaid]

That implies a (sidereal?) clock mechanism, driving the bearing round. So someone must have thought that to important enough to actually implement it..

I wonder though, whether any device of any kind to rotate anything in this system, or do anything that isn't strictly radial, risks undermining the intended behaviour of the pendulum. How can we be sure the rotation isn't caused by, or aided by the additional device?

Same might apply to a centering servo.

Am I right in understanding your suggestion of a coil, as being an air-cored solenoid encompassing either the shaft near the pivot - or an extension of the shaft above the pivot - with a ferrous piece of shaft running up the centre? So when the coil is energised, it tends to pull the shaft in towards the central axis of the solenoid? Now - that solution might also tend to counter any travel of the pivot point across the platform. Maybe it wouldn't need constant centring as it would tend to cause the pivot to self-centre? But the coil might have to be aligned very precisely to the vertical. Just guessing, but it's fascinating.

My guess is that any coil of any real strength, combined with the smallest feasible amount of ferrous material in the pendulum, should ensure that no background field could compete. But I've learned not to dismiss tiny forces based on intuition only, in this project! The fact that a 3 cm deflection of the bob at the end of a 1.2m shaft can exert a strong enough lateral force to bend a solid brass rod in time with the swing, thus driving the pendulum into Lissajous figures, I did not believe until it happened - and I confirmed it with some analysis whose predictions matched experiment quite closely. Stiffening the rod cured the problem and made the whole thing work!

 

[lesaid]

I have discovered one major reason why my electrostatic drive doesn't work. The pivot arm was not properly grounded, and was picking up a charge via leakage from the grounding connection (at the 'hot' end of the earthing resistor). The result - the pivot arm was repelling pieces of the pivot assembly - not enough to rotate the pendulum, but enough to upset the Foucault effect.

This was proven when I attached a grounding wire. Immediately now, on switching on with the pendulum motionless in equilibrium, once a spark jumps, the pendulum pivot assembly, complete with the entire pendulum, rotates until the cage collides with the pivot arm and short-circuits the drive. So an intermittent charge of around 8 kV on a small piece of brass rod exerts enough attractive force on a grounded piece of brass an inch away, to rotate the whole thing, including a 1.4 kg bob, until the bits collide! That says something about the low friction of the pivot I think.

But what is the physics? A positive charge attracted towards a grounded conductor? Are we talking about induced dipoles here? I didn't think of them being significant in grounded conductors, but now I think of it, I can't see why they shouldn't happen.

Not sure what the solution to this is. A non-conducting support arm won't short-circuit the drive, but it will be attracted by a charge. And it seems a grounded conducting arm is also attracted. If I make the pendulum shaft non-conducting, then I have a problem attaching a fine wire to dissipate the charge after each spark - that has to be done at the point of least movement - right at the pivot point. In which case, the charged components need to stay cylindrically symmetrical (and extend above the pivot too) - which means a non-conducting pivot cage and support arm. I'm struggling to think of a non-conducting material I can make this out of that I can both work with, and which is very rigid without being brittle. Any suggestions?

Actually - I have one. If I alternate the driver polarity at the extremity of each swing. Then I don't need to dissipate the charge and the whole shaft can be non conducting, so the problem vanishes. If I can figure out how to switch the driver back and forth between plus and minus maybe 5 kV every second. Timing is easy - don't know about the switching! There goes the 'simplicity' I was hoping for!

 

[sophiecentaur]

Very good point about the 'validity' of the rotating mount.
I am strongly suggesting an iron core for the electromagnet. An air core would produce a weak field all over the place - depending on nearby ferrous objects. Is that what you want? I suggest that you want a well defined external field that is strictly radial, between the centre pole and the ring outside it (just like a loudspeaker). he user ring would screen the field from outside influences. Even the Earth's field would be channeled around the ring, in preference to the air. Which suggests to me that a steel plate (table top) would screen / shunt the Earth's field over the whole of the excursion of the bob. The force would always be towards the centre of oscillation, whatever the plane of oscillation.
Yes I can believe that a very small coupling between two modes of oscillation can cause energy transfer, giving Lissajous figures. The higher Q the oscillation, the more dramatic the effect can be. With a single bar suspension, the period of a lateral oscillation would be slightly different from the period of a longitudinal oscillation and the 'beat' between them (difference frequency) could produce the effect. The massive dome of a cathedral would not suffer from this where your framework could.
The coupled pendulum experiment is a well known example of coupled SHM. There are many links showing this -http://www.hep.man.ac.uk/u/roger/PHYS10302/lecture6.pdf. It rears its ugly head in many forms.

 

[lesaid]

Very good point about the 'validity' of the rotating mount.
I can believe that a very small coupling between two modes of oscillation can cause energy transfer, giving Lissajous figures.

Actually - I don't think that coupling is the problem - though I understand what you are saying. In that version of the pendulum, where in one direction, the bar was very rigid indeed, and the other direction, not quite so rigid - I had lissajous figures where the swing alternated between two straight swing directions, by alternately clockwise and counter-clockwise elliptical movement. BUT if I started the pendulum swinging along one of the 'straight swing' directions, the swing stayed straight. I think, because there was no component of motion in the other 'straight swing' direction. If I started a straight swing in any other direction though, or in a circular swing, the system went into the same lissajous pattern - though the angle between the straight directions varied according to the starting angle.

So to me, it appeared to behave as though there were two independent perpendicular components superimposed at very slightly different frequencies - with no significant energy transfer between them. And an hour of swinging to complete one cycle of the figure.

Sound plausible?

 

[Tom.G]

why wouldn't it also rotate if the pendulum was not swinging?

Rolling friction is less than static friction, or 'stiction' as it is often called.

. What worries me more in this regard is traveling of the pivot point across the platform over time, though this too hasn't shown itself as a problem so long as the swing amplitude isn't allowed to get too high and the platform is kept reasonably level.

Instead of a flat plate supporting the pivot, how about the inside of a spherical section? As in the bottom of a small teacup or drinking glass. There may even be something ready-made along those lines... that is if anyone can come up with the appropriate search terms!

 

[lesaid]

Rolling friction is less than static friction, or 'stiction' as it is often called.

so it is just possible that suspending something that simply vibrates gently might be enough to keep the bearing in motion, and allow it to exhibit this rotation without an actual pendulum? I wonder if that is actually possible.

Instead of a flat plate supporting the pivot, how about the inside of a spherical section? As in the bottom of a small teacup or drinking glass.

I've wondered about that - though not needed to so far. However, I'd be a little wary - whenever the pivot travelled, it would then be on a slope. I've pretty much convinced myself that a slightly sloping platform should not change the behaviour of the pendulum in a material way (so long as it isn't steep enough to make it travel), and this is supported by a cursory experiment. But intuitively, I've got a hard job believing that it really doesn't!

On a different note - slightly surreal - this pendulum works quite well as a geeky clock - tells the time quite accurately to the nearest quarter hour as the bob swings over a card marked out with the hourly rotation intervals. I know it 'should' work - but to be able actually to tell the time by it is a bit 'unreal'! Even though, without a driver, it only works for six hours before running down!

I should try with a heavier weight - should get a longer run time. Though I've no idea how much force the ruby bearing can withstand. This isn't what the ruby probe was designed for! Or the dinner plate piece that the pivot sits on!

 

[Tom.G]

so it is just possible that suspending something that simply vibrates gently might be enough to keep the bearing in motion, and allow it to exhibit this rotation without an actual pendulum? I wonder if that is actually possible.

I've done a similar thing with an old chart recorder. The friction of the pen on the chart was high enough that there was a noticable deadband that lost small changes. Using an Audio Oscillator, I added a little bit of high frequency 'noise' to the signal, just below the level that would show up as pen movement. When a small signal change occured, the sum of the small signal and the added 'noise' was enough to overcome the pen friction. Much more sensitive that way. I don't recall the exact term for the process, but 'stochastic amplification' comes to mind.

 

[sophiecentaur]

So to me, it appeared to behave as though there were two independent perpendicular components superimposed at very slightly different frequencies - with no significant energy transfer between them. And an hour of swinging to complete one cycle of the figure.

You may be right about that. It would depend upon the nature of the figure you are getting, perhaps and whether the main axes of the figure rotate or not.

I like the idea of the 'clock' version of the pendulum. With a large 45° mirror, the clock could appear to be vertical.

 

[lesaid]

I've done a similar thing with an old chart recorder. The friction of the pen on the chart was high enough that there was a noticable deadband that lost small changes. Using an Audio Oscillator, I added a little bit of high frequency 'noise' to the signal, just below the level that would show up as pen movement. When a small signal change occured, the sum of the small signal and the added 'noise' was enough to overcome the pen friction. Much more sensitive that way. I don't recall the exact term for the process, but 'stochastic amplification' comes to mind.

View attachment 211431

clever!

Something like this is also done in gliders I think, to keep the barometric altimeter reading correctly - whereas in powered light aircraft, the engine vibration does the same job.

Now I'm wondering what 'torque' the Foucault effect would exert on a given object, and how good a bearing would have to be to show that effect with simple rotation, and no pendulum. Probably way beyond what is feasible!

 

[lesaid]

You may be right about that. It would depend upon the nature of the figure you are getting, perhaps and whether the main axes of the figure rotate or not.

I like the idea of the 'clock' version of the pendulum. With a large 45° mirror, the clock could appear to be vertical.

The axes don't rotate. Their directions were tied to the orientation of the pivot bar whose flex was causing the problem. The figure was a straight swing which evolved into a clockwise ellipse, becoming circular before collapsing into the other straight direction - then reversed with a counter-clockwise ellipse back to the original direction. Those directions never moved for a given run. But the angle between those directions could be anything from zero to 90 degrees, depending on the way the swing was started.

Now you're giving me ideas of something like a grandfather clock case, with a Foucault pendulum inside and some clever optics to get the image on to the face. That probably means it's time to get to bed! But more seriously, I'm wondering if a geometry of electrodes exists which would nullify the assymetrical effect causing the current problems with the electrostatic driver. I found a geometry that 'balanced out' the moments of inertia so as to be independent of swing direction. I wonder if the equivalent is in principle possible for the electrostatic repulsion. But my intuition says the fact that the force is 'inverse square' perhaps makes it harder. I had in mind - if I bonded the support bar to the pendulum so it would repel, and added other electrodes in the right places, whether I could get the forces to balance out and sum to zero. But I suspect it might not be possible. This will stretch my maths skills I think. But I have read that there is a geometry of masses that can create a region of 'flat' microgravity in the centre. So perhaps it should be possible... Or perhaps this problem will drive me at last into looking seriously at magnets!

Whoever thought a simple pendulum could become so fascinating!

 

[Tom.G]

Whoever thought a simple pendulum could become so fascinating!

Foucault?