The Chaos Machine (Double Pendulum)

Intro: The Chaos Machine (Double Pendulum)

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.

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 2: Top Pendulum - Back

STEP 3: Spacing Block

STEP 4: Top Pendulum Assembly

STEP 5: Bottom Pendulum

STEP 6: 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

STEP 8: Complete Double Pendulum Assembly

STEP 9: CAD Files

Download an AutoCAD .dwg and/or an Alibre Design Xpress assmebly.

STEP 10: Video.

Comments

[mithunashok]

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.

[Irritable_Badger]

The experiment is designed to illustrate that mathematical modeling cannot precisely predict the motion of the pendulum due to variables prior to initiating motion. You can perform the experiment in a vacuum using a robot to replicate the starting conditions and you will still have unpredictability in the motion of the pendulum elements.

You can certainly increase the accuracy of predictions by decreasing the number of variables (as in my example above) but there is always a level of unpredictability present. Which is what it’s all about :)

[surrealista1]

as i know it probably can be described by a fractal

[vmars316]

Hello & Thanks,

I would like to make one of these but on a much smaller scale .

Where could i find miniture ball bearings?

Thanks

btw: 'chaoticpendulums.com' is a dangerous link.

Yikes those 'McMaster-Carr P/N 60355K14' are expensive.

[ProphetMargin]

I'm thinking you add an LED to the bottom hole and turn the lights out!

[armagdn03]

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.

[Sir__Walter]

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.

[DieCastoms]

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.

[sueman2]

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?

[ubr.bzkr]

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.

[mickgoth]

... if light really confuses you that much look up dark energy and dark matter...

[betwys1]

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

[DieCastoms]

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.

[itsthatsguy]

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/>

[BigCountry]

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...

[itsthatsguy]

Lol, good joke, but i have never heard of Tachyons, and quasars are spacel large slow (or non-) moving objects

[Ben5504]

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.

[nightscape_98]

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.

[pacifcace]

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.

[itsthatsguy]

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.