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I started intro today by giving back the very short quizzes they had taken the day before. Instead of going over every problem in detail on the board, I simply selected a few students in advance who understood the problems, and had them go to tables around the room to run a short 5 minute workshop for students to go and explore their mistakes. I think it worked well. In under 5 minutes everyone got their questions answered, and I’m hoping this will empower the students to start to recognize that they don’t need me for all the answers.

After this, we circled back to our work on pendulums from the previous day. Still trying to figure out why it wasn’t linear, I pulled up a few of the pendulums students had made before class, and then compared them to the row of pendulums I made. It turns out I forgot the square in the expression for period, and so all of my pendulums were off by a factor of $\pi$, which itself was a great lesson in the value of experiment, rather than blindly trusting the formula.

a series of pendulums arranged by increasing period.

a parabola that models the relationship between period and length beautifully.

As students looked at the board, we asked if this was linear, and pretty quickly saw it wasn’t. From there, it was a hop skip and a jump from the iphone to geogebra, where we plotted a parabola that fit the data beautifully. At this point, it was easy for the students to rotate this picture 90° CCW in their heads and see that this is exactly the graph we want.

So as a final check, I asked students to predict the period of a pendulum that we would hang from approximately 30 feet up, and then we went outside to test it. Predictions were all around 6 or 7 seconds, when in reality, it was closer to 3 seconds. This was a great moment to think about non linearity again. Our brains see the period linearly, thinking if you triple the length, of the pendulum, the time should triple. However, this is a square root relationship, so when you triple the length, you really only increase the period by a factor of $\sqrt{3}$.

Then we wrapped everything up with a webassign based lab (note to self—rigorously check WA assignments before deploying), on linear modeling, which was a bit too much for some in the class. Ah well.

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