Repost: Physics with Toaster Strudels March 13, 2011
Posted by mareserinitatis in food/cooking, math, physics.Tags: art, food, frosting, lissajous, oscilloscope, toaster strudel
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In my love all things Pillsbury (does it surprise anyone that I used to work in Pillsbury Hall, of all places?), I became addicted quite a while ago to the toaster strudels. Very early on, the younger son decided that his toaster strudels were actually canvases upon which his mother was supposed to create pictures. Apparently, he’s not the first to have this idea. But there is only so much detail one can get before the frosting starts running low.
One day, as I was messing around, I came up with the idea of making Lissajous figures. This was not particularly impressive to my younger offspring as he would rather I draw cars, tractors, trains, or Transformers. I, however, thought it was pretty cool.
Lissajous figures are figures created on an oscilloscope when you have two signals that are harmonics. One of the signals can have a fundamental frequency, while the other is a multiple (n). This sort of arrangement makes the figure look like a large loop of string with (n-1) crossings and n “loops”. So a fundamental frequency with it’s second harmonic would create a figure 8 – one crossing and two loops. The Science Museum of Minnesota has a fascinating demonstration using a rod that you vibrate. Looking at the end of the rod, you can see the same figures depending on how you torque it initially.
You don’t have to stick with the fundamental frequency, however. You can have a second harmonic in one direction and a third in the other. That’s what I chose to do with my toaster strudel. I’ve also tried to get the 3rd harmonic mixed with the fourth, but that seems to require more frosting than is available in the little packet…and I’m not sure I’m willing to have a frostingless toaster strudel down the line just for the sake of art.
I’m thinking that the next thing I could try would be free-body diagrams…preferably on inclined planes. Or perhaps an XKCD cartoon.
Physics with toaster strudels
In case you’re interested, Wolfram has a nice set of 2- and 3-D visualizations of Lissajous figures.
I also blog at Engineer Blogs, home away from home to some of the best engineering blogs.
I loved Lissajous figures in high school physics. In fact, that was one of the things that set me on my path to teaching physics as a career!