### Drawing Board

#### by Aiona

Last week I snuck up to drawing board a few minutes after closing with one of my closest friends, Daniel, who is also one of the biggest physics geeks I know. In the void and lonely mezzanine we boldly experimented with the one thing we were explicitly told never to do… we moved the weight. It was the dawn of a new fascination with this simple exhibit, and its complex mathematical properties. The following is a brief geek out session about the physics of drawing board: When we first learned how to facilitate this exhibit, Sarah told us about how the board has three degrees of freedom, movement along the x-axis, movement along the y-axis, and torque. When the board is moving along both the x and y axes it creates a circle, while torque will create figure eights and more complex patterns. As friction slows the swinging of this giant rectangular pendulum, the shapes become smaller and smaller until they shrink to a point and all that is left is a crazy psychedelic image. This type of pattern is called a harmonogram, and here’s a really nifty applet where you can play with them: http://www.comsewogueyouthclub.net/encyclo/640×4801.html. The drawing board at the Exploratorium is basically a giant real life harmonogram maker, except that it’s been specifically tuned to have certain properties. According to the museum website, the weight on the board and the length of the chains are specifically designed so that the period of the torque is twice the period of the pendulum motion. You can destroy this by sitting (very very still) on the drawing board while it’s moving. The result is a more complex harmonogram that can do more loops than just a figure eight. Moving the weight off center will cause the pattern to morph more rapidly than normal. I have no idea why that is, but please please post a response if you do. I hypothesize that the torque is not entirely independent of the pendulum motion and that motion of one sort either decays faster than the others, or can be translated into it. I also noticed that if I start the drawing board moving along only one axis it will start out as a line, morph into a circle, and end up moving in a line along the other axis. Why does it do that? Please, please, physics geeks of the museum, answer all my questions about drawing board!

I have no answers, only questions. Can you please check the link you posted? It doesn’t work for me.

try this link:

http://www.coolmath.com/coolthings/encyclogram/index.html

Theory behind hypothesis: it’s long and complicated. I’ll divulge if my prediction is correct. Otherwise it would waste your time. Basically, I think you are storing energy on two stable axes.

Prediction: There are two perpendicular stable axes (axes in which a line will stay a line), but they are not correlated to the long or short side of the drawing board. Move the board straight out like you described. Such that, the movement begins as a line, morphs to a circle, and then becomes another line, which is perpendicular to the first. Now notice that the second line is shorter than the first. This is not only because the pendulum is damped. The closer you are to a stable axis the shorter this second line will be. If they are close in length then you are near 45° from a stable axis. If you connect the four points of these two lines you will make a rhombus, or 4 right triangles. One of the sides of the rhombus, or hypotenuse of the triangles is the direction of the stable axis. Try one (there are only two options). If the ratio of the line’s lengths gets closer to 1 then you picked the wrong one, otherwise you should be very close to the stable axis. Remember to just pull the pendulum straight out and let go, without displacing it along it’s rotational degree of freedom. Good luck.

BTW, great link. When I would use the drawing board I always thought the pictures looked like 2d projections of a 3d object. If you set the x1 and y1 amplitudes to 0, and then change the phase of either x2 or y2 it gives the illusion you are rotating the object, which is just plain rad.