Instructables

The Chaos Machine (Double Pendulum)

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Every physics department needs a double pendulum, so here's how I built ours. The big improvement is that the bottom pendulum can be locked in place. This turns the chaotic double pendulum into a non-chaotic physical pendulum.

I'm going to be lazy and skip writing a big long introduction or explanation for this. The Wikipedia article on chaos thoery is pretty good and explains how chaotic systems are sensitive to initial conditions. The mathematics are too complex to accurately reproduce here, but the links below can show them correctly:

http://en.wikipedia.org/wiki/Double_pendulum

http://en.wikipedia.org/wiki/Pendulum_%28mathematics%29

http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

http://www.myphysicslab.com/dbl_pendulum.html (simulation)

http://www.chaoticpendulums.com/chaos-theory-a9.html (simple explanation of chaos theory)

Here's a neat version made from two square plates:

http://www.physics.usyd.edu.au/~wheat/sdpend/

You can buy a double pendulum from chaoticpendulums.com, but it's more fun to build your own. Look at the pictures, look at the CAD files, watch the video, and then go make one.

Support Amazon.com for sponsoring this science fair contest, buy ball bearings online.

Safety

Standard shop and power tool warnings apply, but I have to provide a warning specific to the double pendulum. The bottom pendulum can get moving very fast and because it's chaotic, it's unpredictable. If your hand or face is in the wrong place and the wrong time, you can get seriously hurt. The best thing to do is to set it in motion and then stay out of the plane of rotation.

I fixed the video! Sorry about that. It's viewable in step 10.
 
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Step 1: Top Pendulum - Front

This aluminum bar is half of the top pendulum. Another similar bar forms the second half. The ball bearings are 3/8" ID x 7/8" OD x 7/32" wide (McMaster-Carr P/N 60355K14) and are held in place by a #8-32 set screw. There are four bottom tapped #8-32 holes for the screws that hold the top pendulum together. There's one more #8-32 through hole for the bottom pendulum pivot. Finally, there's a 0.311" hole for the socket head shoulder bolt.

Step 3: Spacing Block

Picture of Spacing Block

Step 6: Bottom Pendulum Pivot

Picture of Bottom Pendulum Pivot
This is the pivot for the bottom pendulum. The length is the same as the width of the top pendulum spacing block.

Step 7: Bottom Pendulum Assembly

Bottom_Pendulum_Assembly_8.JPG
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mithunashok5 years ago
Wow...that was cool maannn....Have any one tried this again? I am sure its called "chaos machine" bcoz no matter any no of time u try,its not going to trace this path.Its cool.... Tell me if anyone can express it mathematically or if anyone could write an algorithm to predict its motion.

as i know it probably can be described by a fractal

armagdn0310 months ago
This is a parametric oscillation. It can be made non chaotic through balance of variables with respect to harmonics. I am still not convinced through my own study that chaos is ever really chaos.
Hey, great machine. Wondering if using something heavier such as steel would still make it work fine, or would it work just so long as the two bars weight are in proportion with each other? Thanks.


DieCastoms5 years ago
Ok, I am not a scientist, I do not claim to be. This should be taken as an honestly curious question and not as an attack on any one individual person or comment. That being said, several of you have stated that it takes an infinite amount of energy to accelerate any mass to light speed. I can accept that. It is an obvious fact that light travels at light speed, otherwise the phrase light speed would be kind of stupid wouldn't it. I would assume that light has mass since if it did not, the gravity from a black hole could not overpower it? Gravity has been proven to affect the trajectory of light. So if light DOES have mass, and light DOES travel at light speed, then accelerating a mass to light speed IS NOT impossible. Again, this is for DISCUSSION. It is not an attack on any individual or his or her post. Mike, at DC.
Then why does light not kill you when it hits you?
since it is moving so fast the small amount of mass doesn't matter. Like it would have to be 1000000000000000000000000000000000000000000000000000000000000
000000000000000000000000000000
0000000000000000000000000000000000
00000000000000000000000000000000000000000N

i do like your fact and will share it with my friends. I simply ask for your view. Do you happen to have a blog or video channel of some sort i can subscribe to, so to hear more of your views?
First, because many particles that small go right through you like x-rays. Second, the particles that would impact the particles in your body would likely have very small amounts of kinetic energy.
Because of this, the small amount of mass would matter as the speed of light is 299,792,458 m / s. now using the formula:

ke (kinetic energy) = (1/2)M*v^2

where M = mass and V = velocity. A tiny particle such as an alpha particle which weighs about 6.64424 × 10^-27 kg (and is much larger than a photon) moving near the speed of light would have kinetic energy equal to only about
2.9858*10^-10 Joules. which is equivalent to around 3*10^-9 newton meters.
you cant even feel it.
... if light really confuses you that much look up dark energy and dark matter...
The equation for which Einstein is remembered in the popular imagination is this: E = m.c^2 This expresses the idea that mass and energy can be interchanged. Another physics whizz came up with this equation: E = h.f which expresses the idea that e.m waves like light carry a certain amount of energy in chunks which increase with increasing frequency. This chunk is labeled the quantum. Mixing the two ideas: the unit of energy can be worked out for light of any particular color: less for red, more for blue, more still for ultraviolet, much more still for X-rays. So we can suppose that a quantum of light can act like a particular mass, even though it is weightless. This lets you work with the idea of a ray of star light heading towards your eye, bending towards the Sun, if its path is close. Usually the Sun is too bright to see this effect, but what if you wait for a Solar eclipse? /brian whatcott
I cannot say that I completely understand your explanation, but I can say that it might be the simplest and most coherent (for me) explanation I have seen yet for this subject.

In the case of E=MC^2, Energy = Mass times the Constant (speed of light) squared. This refers to the amount of energy that can be released by a given amount of mass if ALL energy could be released, 100% efficiently.

In your post you mention E=hf and you also mention e.m waves. Can you expand on those two, please?

I appreciate that you took the time to post this! Thank you.


Mike from DieCastoms.
I see where your coming from, but light is made of photons, which, so far, have apparently no mass although its not 100% since measurement devices might not be able to weigh something so small.<br/><br/>"That being said, several of you have stated that it takes an infinite amount of energy to accelerate any mass to light speed. I can accept that."<br/><br/>you kinda contradicted yourself, if it takes an unlimited amount of energy to move things at light speed, then why can an led and a double a move photons (Which you said have mass) do it =)<br/><br/>Not trying to be a jerk, just throwing my 2 bits are your discussion.<br/>
Don't tachyons, or is it quasars? travel faster than light? And have mass?

Sometimes I think the weeds in mu garden grow faster than light...
Lol, good joke, but i have never heard of Tachyons, and quasars are spacel large slow (or non-) moving objects
You bring up a very nice issue. We've moved past special relativity and are now on general relativity =)

You're absolutely right: for a long time, people had difficulty combining the "massless-ness" of light with the fact that light can be deflected by massive objects (which is a proven phenomenon). I'll see what I can do to explain.

Imagine a large, squishy mattress. When you place a large object on that mattress, like a bowling ball, it sinks into the mattress and creates a dip all around it. If you were then to place a marble somewhere nearby on the mattress, it would roll toward the bowling ball because of the dip.

This is a really good analogy for the way that space behaves in the presence of an object with mass. Around any large object, like the sun, space is distorted, and nearby objects, like the planets, feel the effect of that distortion (they tend to "roll toward" the sun). Unfortunately, it's much harder to visualize in three dimensions.

Okay, so let's look at how it affects light. Going back to the bowling ball on the mattress: what would happen if you tried to roll a marble past the bowling ball? It would hit the dip in the mattress and curve toward the bowling ball. If you rolled it fast enough, or if the dip wasn't very deep, it would curve a little bit but still be able to make it back out of the dip, but now traveling in a slightly different direction. This is what happens to light going around massive objects in space, like a galaxy. This phenomenon is called "gravitational lensing", because the galaxy redirects light, just like a lens can do.

With black holes, imagine the dip in the mattress is very, very deep, so deep that no matter how fast you roll the marble, in can't make it back up the other side, but instead spirals around the dip until it reaches the center. This is what happens with black holes because they are so massive compared to anything else.

So, long discussion, but in summary: yes, gravity does affect the trajectory of light, but not because light has mass. Rather, mass changes the shape of the space around it, and light follows that shape, and is deflected.
Correction, Light does have mass, very small but it is there. Light is made of a sub atomic partial called a photon. It has 3 dimensions and has mass. Relativity hasn't caught up with this yet nor has the math to explain it. The discussion here is as old as einstien and has been rendered useless though not less thought provoking. Light is energy is matter. All radiation has mass because it is a radiated partical of a larger whole. Seems a lot of people forget that.
A single photon has no mass, a system of photons has mass. It's an odd property that crops up from the math of relativity, but it can be easily shown that to travel at the speed of light an object must have no mass, and it can also be shown that a system of these massless particles taken together does in fact have mass.
Do you guys have an cited works, because, i for one, have never heard of any solid evidence that a photon or a system of photons has mass.
Well, just about any Modern Physics textbook will contain a discussion (and probably a few problems relating to) the mathematical proof of a single photon being massless but a system of them not, but specifically I can offer this.

Taken from Paul A. Tipler and Ralph A. Llewellyn's book Modern Physics (5th Edition), Example 2-12 from page 90:

Rest Energy of a System of Photons
Remember that the rest energy of a system of particles is not the sum of the rest energies of the individual particles if they move relative to one another. This applies to photons too! Suppose two photons, one with energy 5 MeV and the second with energy 2 MeV, approach each other along the x axis. What is the rest energy of this system?

Solution:
The momentum of the 5-MeV photon is (from equation 2-35, E=pc for m=0) px= 5MeV/c and that of the 2-MeV photon is px= -2MeV/c. Thus, the energy of the system is E = 5 MeV + 2 MeV = 7 MeV and its momentum is p = 5 MeV/c - 2 MeV/c = 3 MeV/c.

From equation 2-32 ( (mc2)2 = E2 - (pc)2 ) the system's rest energy is mc2 = ((7 MeV)2 - (3 MeV)2).5 = 6.3 MeV!!

(What this means, then, is the mass of a system of photons moving relative to one another must be non-zero, i.e., the system has mass)
Point taken, thanks for some back-up info.
Closet_RAt6 years ago
The real killer (the reason the patterns cannot be predicted) about trying to figure out the patterns is that scientific theories are usually proven wrong.

While this is *relatively* trivial when it comes to whether the Earth is flat, or the moon is made of cheese, it does pop up when to matters that can be proven on the spot (such as this experiment).

I became irate at this when I asked my biology teacher why books say it's impossible to travel at the speed of light. His answer was that at the speed of light mass becomes infinite. When I challenged him that as we've never gone that fast before, how would anyone know, his reply was that it was just a proven fact, just like how it's impossible to twirl your arms in opposite directions. When I showed him that I could do just that, he said I was doing it "wrong", because it's physically impossible.

So, I showed him a second time, explaining that I'd heard that one before, and practiced doing so for a few minutes (based on my own theory) before nailing it perfectly.

But he still wouldn't budge.

For the record, I'm referring to pointing your fingers at each other (arms held roughly at shoulder level, and spinning from the elbows to make the fingers trace the same circle in opposite directions. People will normally follow one arm on accident within the first few minutes. But I have proven that if you plot out the course the opposing arm needs to take in your head, and keep focussed on that objective while subconsciously twirling the dominant arm, then it is quite easily possible. I now actually have to let my arms do it the normal way...

Science is chaos, zero predictability (go Doctor Malcolm!!!)
It's impossible to travel at the speed of light because it would require an infinite amount of energy to reach that speed.

Relativistic energy is defined as E=γmc2, where γ = 1 / Sqrt(1-(v/c)2). (v is the object's velocity, and c is the speed of light). If the velocity were equal to the speed of light, then γ would equal 1 / 0, which is infinite.

The best analogy I can give you is accelerating a car. It takes very little horsepower to get a car moving from rest to, say, 20 mph. However, once the car is moving 60 mph, you need much more horsepower to get it up to 80, even though you're technically still accelerating by 20 mph. Because the car already has a large amount of momentum, you need more energy to change that momentum, even if it's in the same direction. To get up to the speed of light, it's not only difficult to accelerate to that point, it's impossible, because there simply isn't enough energy in the universe.
well it is possible for an object to have infinite mass. It did happen in the big bang and then it moved so there is enough energy in the universe too move an abject with infinite mass. Also when a macro sized object approaches the speed of light its mass and density gets so great that it would turn into sort of a black hole. So it would modify the speed of light to what ever speed it happened to be going because light would be sucked in and wouldn't be able to escape. Will someone plz. tell me how my glob of odd logic is mistaken thanks.
How do we knowthat. has anything traveled the speed of light then turned into a black hole? Do we have proof of that? But here's something to think about. If you're driving faster than the speed of light and you turn your headlights on, what happens? The speed of light is just a thing. Just like the sound barrier is. We broke that and we didn't all die. The same should be true for the "light barrier". How does something gain infinite mass? Just because light isn't traveling as fast as it doesn't mean it can't be seen. Jets can fly faster than the speed of sound, but we still hear them.
ubr.bzkr temp5 years ago
IF you go faster than the speed of light in a car and turn the headlights on you would see nothing but darkness because the light would be going behind you because you are going faster than it. read Michio Kakus "Physics of the Impossible" it answers alot of questions.
You are wrong. Light is always the same speed no matter how fast you are going. If you did turn you headlights on, they would act like perfectly normal headlights and speed away from you at the speed of light. Read Einstein's theory of relativity, it answers a lot of questions.
Which is why you cant go faster then the speed of light. thats why i put IF.
Anthony312 temp3 years ago
The speed of light is NOTHING like the sound barrier. It CANNOT be broken. It is a constant of the universe. It is a speed limit. The faster something goes, the more massive it is. You weigh more while you run then while you sit down. At the speed of light, you gain infinite mass, but because that is impossible, it is impossible to go at the speed of light. This is proven in particle accelerators. Yes, we have sent things at near the speed of light and created black holes in particle accelerators. There's your proof.
The big bang did not have infinite mass, if it i did, then the universe today would be pure mass and there would be no empty space. The universe had infinite DENSITY and infintesimal size. And the big bang didn't move, it stayed the same place the entire time. Its confusing, but the big bang happened at every point in space simultaneously. Even the space you occupy now was once the big bang. Black holes don't modify the speed of light at all, so your logic is mistaken.
it's impossible to accelerate to the speed of light maybe, but what if the object is already going the speed of light?
Well, it's also impossible to have an object traveling at the speed of light to begin with. Such an object would have an infinite amount of energy, and there simply isn't that much energy in the universe. Another thought: an object traveling at the speed of light would have to have accelerated to that speed at some point.
Everything moves at the speed of light. Thinking of relativity, if you look at the speed of light and the objects around light, then you have the objects in reference to the light, technically, no object can't go faster than the speed of light. The reason this is true is because the light can be seen as stationary in space, while the rest of space is hurling off in the direction of the light's source (which ran away from it, as well; poor light). Also, the speed of light can be 0m/s. This case would be evident when light is in the center of a black hole. It has no speed/velocity because the mass is trapping it (and since the black holes are so massive, once it gets back in it can't get back out). If the speed of light can be 0m/s, then anything can move at the speed of light.
the speed of light can never be zero.  when light is pulled into a black hole, it’s path is curved and it’s energy is sapped (meaning it’s frequency changes), but the speed stays the same.

when we say “inside” a black hole, what we mean is the space beyond the event horizon because this is the point at which light and matter can not escape; they are gone from the observable universe.  but just because we can’t see it doesn’t mean the matter in that space doesn’t exist.

if you were able to observe the “inside” of a black hole, it might look similar to the “outside”.  you would see matter and light in an infinite orbit around the singularity, just like you see the orbit of matter and light around the outside of the black hole.

you would also see the apparent horizon…  the region close to the event horizon where matter can almost just escape, but never does, and may not be able to reach the event horizon because in-falling matter prevents it from going that far.  in this thin region is the radiation and matter and light that entered the black hole and didn’t fall into the singularity because it had enough angular velocity to enter into an orbit.  anything passing through this area is instantly vaporized because it’s so bright and super concentrated.

anyway, the point is that the light that falls into a black hole does not simply stop.  when light comes in contact with something it is either absorbed or reflected.  the light that enters a black hole is either trapped in an eternal orbit (traveling at the speed of light), or it falls into the singularity and is absorbed.

by the way, my theory of why the speed of light is relative is that the local nature of space and time is altered at speed.  to illustrate my point, imagine a piece of paper is a two dimensional universe with 2d humans living on it.  now wrap that paper around a basketball.  their universe is now curved, but they don’t realize it.  they move in a straight line and perceive it as a straight line, but to us, we can see that their path is actually curved.  we changed their universe, but to someone inside that universe, nothing happened.  it’s the same as time slowing down the faster you go.  you perceive time as moving at the same rate, but an outside observer knows that your time is slower than his.  just like you will always measure the speed of light as 186,282 miles/sec (a measure of distance over time) no matter how fast you’re moving because space and time will warp to make it so.
yeah thats a good thought. if lights speed was technaly zero because everythign else was moving relitive than it then if you went "faster" than the speed of light your speed relitive to light would be zero or less than zero. like negitive energy. If you think of it that way it makes sense why matter cant go faster than light because it already is.
Finally somebody understands. Thank you.
jillg Ben55045 years ago
or it could have no mass
Ben5504 jillg5 years ago
That's true, but what kind of object could you have that doesn't have mass. On a related note, there's a lot of current research aimed at determining whether or not neutrinos have mass. These are particles that have been detected moving at the speed of light (or at least extremely close to it) and so there is debate as to whether they have mass (and thus travel just below the speed of light) or if they have no mass (and travel at the speed of light).
mirzah1 Ben55043 years ago
What about this theory- as electrons are accelerated up to very near light speed in for instance a transmitting antenna they undergo a change in state and are transformed into energy -a wave in fact- no mass and able to travel at light speed, when they slow slightly as for instannce on striking a receiving antenna they regain their mass and revert to electrons again. Might explain the dual wave\particle mystery, or not?
sonaps Ben55045 years ago
Dark Matter.
jillg Ben55045 years ago
there is also a theroy that supports the existence of tachyons, particles that move faster than the speed of light but cannot move slower than it
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