Foucault's Pendulum Recreation for Physics Project

[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 occurred, 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 occurred, 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?

 

[Tom.G]

re. spherical vs flat support

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.

The idea was that a spherical support would cancel out any imperfections over a rotation cycle and keep the center of the bob path fixed over the excitation device ('electrostatic motor'), at least on average.

p.s. Could you post a photo of the contraption?

 

[lesaid]

Could you post a photo of the contraption?

Here goes - hopefully it won't be too large for the forum ...

I have more design details - if anyone wants to try to put something like this together and would like more detail, please let me know.

From top left, clockwise
1. The pivot assembly. White 'blob' is polymorph that holds the china platform in place and prevents the pivot from sliding off it. Frame is made from pieces of brass bar cross section 13x3 mm, soldered together with the aid of a small blowtorch. Don't look too closely at the solder quality - I'm used to a soldering iron, not a blowtorch for soldering! Assembly was done with the aid of lots of (now charred) temporary wooden jigs and clamps. The support bar is made from two lengths of bar, one perpendicular to the other, to form a 'T' cross section. This was the stiffening required to remove lissajous figures, after which the pendulum worked. Shaft is 3 mm brass rod, joined with M4 hex standoff nuts with bar soldered into the ends, and with M4 threaded brass rod to provide height adjustment. The ruby probe is one of these : http://www.renishaw.com/shop/Product.aspx?Product=A-5000-7808.

2. The bob, slung on an M4 threaded brass hook screwed into a hex nut on the bottom of the shaft. below is the card marked off in 'hourly' intervals.

3. The base, underneath the card. The driver electrode is screwed into an acrylic sheet, and (not visible) attached to a screened EHT lead going to the power supply. The reason for the long bolt is to get the action point well away from the feeder. Initially, with an unscreened feeder and a short bolt, the pendulum would tend to swing in line with the feeder cable! The bob is a brass-encapsulated lead clock weight with a bolt and domed nut glued to the bottom, matching the driver electrode.

4. The pivot assembly on its own, showing the pivot point. the probe is screwed into an M2 hexagonal nut, which in turn is screwed on to an M2 bolt whose head is soldered to an M4 nut that joins the frame pieces.

This is the schematic from which I constructed the whole thing. The attachment of the ruby probe to the frame is not quite the same as the final device, but otherwise it is accurate.

 

[sophiecentaur]

The axes don't rotate. Their directions were tied to the orientation of the pivot bar whose flex was causing the problem.

The simplest Lissajous figures are generated with totally independent X and Y inputs (two separate generators with different phases or frequencies). Actually, two nominally independent High Q oscillators can 'see' each other through all sorts of electrical paths and you can get interaction (beating) between them. In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support. The Q factor is only in the order of hundreds or a few thousand (?). Displacement in one direction (particularly when you have a single supporting rod / beam can cause a displacement in the other direction. Twisting the beam can cause it to shorten. If there is any asymmetry in the support, a change in length can cause an offset in the position of the pivot in the line of the beam. (This will depend on the rigidity of the supports, of course) It would be pretty easy to force this to happen by using a low modulus, asymmetrical support. In your case, you improved things by increasing stiffness, which reduced the coupling. The clincher, I think, is when the lissajous figures have maximum deviation (possibly almost a straight line in one direction) and then it changes to another direction every cycle (walking through) - showing that the energy has left one mode and gone to the other one - and back again. It's quite possible that your arrangement has always been good enough to eliminate this beat over the operating time of the pendulum so my idea may just not be relevant. If you were to sort the oscillation in the direction of the axis, was there any oscillation induced across the beam? That would have to be due to coupling but only if the beam were not being rotated by the earth, of course and the gyroscopic effect came in.

 

[lesaid]

The simplest Lissajous figures are generated with totally independent X and Y inputs (two separate generators with different phases or frequencies). Actually, two nominally independent High Q oscillators can 'see' each other through all sorts of electrical paths and you can get interaction (beating) between them. In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support. The Q factor is only in the order of hundreds or a few thousand (?). Displacement in one direction (particularly when you have a single supporting rod / beam can cause a displacement in the other direction. Twisting the beam can cause it to shorten. If there is any asymmetry in the support, a change in length can cause an offset in the position of the pivot in the line of the beam. (This will depend on the rigidity of the supports, of course) It would be pretty easy to force this to happen by using a low modulus, asymmetrical support. In your case, you improved things by increasing stiffness, which reduced the coupling. The clincher, I think, is when the lissajous figures have maximum deviation (possibly almost a straight line in one direction) and then it changes to another direction every cycle (walking through) - showing that the energy has left one mode and gone to the other one - and back again. It's quite possible that your arrangement has always been good enough to eliminate this beat over the operating time of the pendulum so my idea may just not be relevant. If you were to sort the oscillation in the direction of the axis, was there any oscillation induced across the beam? That would have to be due to coupling but only if the beam were not being rotated by the earth, of course and the gyroscopic effect came in.

Trying to get my head around the implications of what you said ...

In this case, there has to be some coupling between the two oscillators because they are connected to the same beam support.

that makes sense, in principle. In this case though, the difference in 'flexibility' must be huge. In one direction, a relatively thin (3 mm) brass bar is bending over a six inch or so length - I was able (with the aid of a microscope) to estimate the spring constant quite easily. In the other direction, a displacement requires compressing the bar lengthways and/or distorting a pretty robust wooden beam to which the bar was clamped.

The behaviour I was seeing is exactly as described in https://en.wikipedia.org/wiki/Lissajous_curve under the subheading "Application for the case of a=b", though to complete a whole cycle took 58 minutes. If the swing was started off circular, that is the pattern it settled into. The stable directions did not move - the pattern stayed the same, including its orientation, right through the decay over five cycles or so. If I recollect rightly (can't do this experiment any longer having stiffened the bar!), if the swing was started as a straight swing half way between the two 'straight swing' directions, it would become elliptical and develop into the same pattern as if it had been started as a circular swing. Intermediate initial swing directions produced two stable swings that were not perpendicular - the angle depending on the direction of the initial swing. In all cases, the 'straight swing' directions, once established, did not move at all.

A quick calculation gives a Q of just over $10^5$, based on a swing period of 2.2s and a decay constant of about $1.33 * 10^{-5}$ - which I still find unbelievably high (if I've got it right!).

I tried modelling this behaviour in two different ways, using the measured spring constant, and predicting the frequency of oscillation for the measured spring constant, and a dramatically higher value. Calculating the elapsed time for the two frequencies to drift out of phase and back, through a whole cycle, came to 36 and 38 minutes for the two methods. I think this is close enough to the experimental 58 minutes to support the models, given the sensitivity of this system and the simplifications (one method involved modelling a longer pendulum such that the movement at the original pivot point matched the measured flex in the bar - the other was through setting up equations of motion and using eigenvalues to find the frequency).

I am practising newly learned skills here, so being a little wary of making silly errors, but these results seem to me to make sense.

I am wishing now that I had taken the time to try to measure the spring constant of the stiffened version of the bar before mounting it back into the pendulum. I suspect that flex would have been too small for me to detect.

I am thinking that the reason the swing decays into a small circular motion before finally stopping, is perhaps because the direction with the larger swing will decay faster than that with the lower swing, so the ratio of amplitudes of swing in the different directions might approach 1 as the amplitude approaches zero? Or perhaps it is due to transfer of energy, and if this system could run for 24 hours instead of 6, I might see a cyclic behaviour. Not sure how I tell which behaviour I'm seeing?

But now, since the fix, if I start with a circular swing - it just decays into smaller circles until, hours later, it finally comes to rest.

Learning a lot with this project!

 

[sophiecentaur]

@lesaid From what you say about your setup, the mods you did have reduced or eliminated the problem so perhaps you needn't worry about this.
It would not be too hard for you to retro fit a similar arrangement to your original. It struck me that a rigid plate, mounted on a round bar, with rubber each side, would give two different values of swing period and if you fix the rod at one end only, that would provide the coupling from one mode to the other. There are many alternative arrangements that you could probably incorporate in your setup. Perhaps a 'wedge' of resilient material, mounted diagonally, could provide some coupling.
Just to reiterate my point: if you start the oscillation in just one plane and the other mode starts up significantly within less than a few hours, then there must be some coupling. The Wiki article doesn't discuss coupled oscillations, afaics and that is another level of difficulty. With coupling, the amplitudes of each component change, according to the coupling coefficient.

 

[lesaid]

Thank you for those ideas - this project is spawning off things to think about in every direction! Pity I've got to move my focus primarily to my scheduled studies after this weekend - but I'll keep on at this in the background. I'm building up a growing list of things to explore!

I am not giving up yet on a simple drive with no electronics - I'm going to do a bit more on the electrostatic approach before moving to magnets. But - a question. It seems that the pivot assembly and the support bar experience a mutual force, whether they both have a charge at the same potential, or when just one is charged and the other is grounded. I presume the latter is because of induced dipoles.

So - it seems to me that two conductors each with the same charge will repel each other slightly less than Coulomb's law would predict, as induced dipoles in each conductor should add a small attractive force into the mix. And if the charges are opposite, they should attract slightly more than the prediction as both forces will now be attractive and should add together.

I haven't heard of this before so I suspect I'm wrong. But does this make sense?

If so, might be interesting to try to measure the discrepancy with a torsion balance or similar. I'll also have a go at trying to calculate what those forces should be, though I'm not sure yet how to work out the forces between charged bodies that can't be approximated as point masses! I suppose I need to start by understanding the charge distribution through and on the surface of the body. Perhaps I need to get through the 'Maxwell' part of my course first!

A work-around for this problem on the pendulum was suggested by someone else - to put the 60 Gohm resistor in the pendulum shaft just above the bob - so the entire upper shaft and pivot assembly can be grounded. Then all electrostatic forces at the pivot have to disappear.

 

[SPW]

(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

Hi, one of the easiest ways to obtain a low friction pivot for your project is to use a universal joint. They are available in very small sizes for around £10 - £12. You can also use a solid bar instead of string/cord for greater accuracy.

 

[lesaid]

Hi, one of the easiest ways to obtain a low friction pivot for your project is to use a universal joint. They are available in very small sizes for around £10 - £12. You can also use a solid bar instead of string/cord for greater accuracy.

Hi! Thanks for joining in!

Actually - I am using a solid bar for exactly that reason - I found it a great improvement on a cord! My pivot is a ruby bearing sitting on a hard platform - if you scroll up a few posts, you'll find photographs :) With a shaft of only about a metre, I didn't think any kind of 'ordinary' joint would be good enough.

What I have now works very nicely - shows the Foucault effect over up to six hours while it decays (unpowered). Currently looking at how to implement an electrostatic driver.

Edit : Sorry - misunderstood - you were replying to the first post in the thread? Ignore my comment if it isn't relevant!

 

[SPW]

To obtain a low friction 360degree pivot you could use a Universal Joint. These can be bought for around £10. Another possibility is to use a Neodymium magnet. Both of these solutions would also allow you to use a metal rod instead of string, which would be more accurate. I hope this is useful.

S.P.W.

 

[SPW]

Hi again, if you want run the experiment for 24hrs you could use an escapement, such as is used to keep an analogue clock ticking. Depending on how good you are at woodwork, they're quite simple to make. Google "escapement animations". Alternatively, you could adapt "the perpetual pendulum" which uses magnetic induction to give your pendulum a kick. It's not that complicated. It uses a couple of coils. 1 to discharge the current at just the right time & the other works like an electromagnet to give the kick. Here's a model & curcuit diagram. http://www.bowdenshobbycircuits.info/swinger.html

Hope that's inspired you. Keep your thread updated, I'd love to see the finished project.
S.P.W.