Day 1 of Oscillations (Day 1 of a Unit of Oscillations of Waves; Day 1 of the 2nd Semester physics)

**Unit Motivation**: I began this unit with a rather silly demonstration. I had a function generator send a sinusoidal signal into a speaker; an oscilloscope showed what was happening with the electrical signal. I started with the frequency set low enough so that we could see the speaker moving, but not hear it. In front of the speaker, I placed a microphone which then plotted the pressure changes. After briefly orienting students to the setup, I used a fairly standard, “What do you notice? What are you wondering?” line of questioning. This ultimately led into a brief orientation to what we would be learning this semester (oscillations, waves, sound, electricity, etc). I also used this as an opportunity to motivate why we would spend this week studying two simple (and boring) oscillating systems (pendulum and mass-spring). With these, we didn’t need any specialized equipment to observe these systems– either to understand its mechanisms or to take careful measurements. I alluded that learning about these systems would pay off in terms of understanding more interesting things like sound, electricity, and light.**Observing Kinematics Graphs for SHM**: As a demo, I showed students how to setup a vertical oscillating spring. [Side Note: In this class, we don’t set up any lab equipment for them; students must go get what they need, setup any apparatus, any put things away. Last semester, I had done some setup for students, especially when it involved rods and clamps. But this semester, I am having students even do those, so students are becoming more familiar with how to quickly set up things with table clamps and right angle clamps.] While playing with the spring, I also briefly introduced some language students were familiar with from last semester, such as equilibrium position and (linear) restoring force. Anyway, with a motion detector, we observed the motion of the mass-spring system and I recorded just the position vs. time graph. Students were then given a laboratory exploration to first predict and then observe the velocity vs time graph and acceleration vs time graph, focusing on how they line up. There were some additional questions for them to discuss about where is it moving fastest, where is the velocity zero, where is the acceleration greatest, etc.**Direction Instruction on Sinusoidal Graphs:**Back together as a class for some direct instruction, I introduced sinusoidal functions a way of mathematically describing the graphs they’d just seen. I used a Desmos file to show them what effect the parameters had on the shape of the graph (corresponding to Amplitude and Period), pointing out that the mathematics allows us to control Amplitude and period separately. Some of this involved reminding them about frequency and period which they had learned last semester for circular motion, and part of this involved making more connections to their reading assignment.-
**Modeling and Practicing a****Logger Pro Lab Skill-Curve Fits for Sine Graphs:**Next, **Clicker Question and Mini Exploration-Does Amplitude effect Period**: Back as a whole class, the question was posed to students, how the period would change if the amplitude was increased? [I didn’t actually use the words period or amplitude… we watched the vertical spring again, and I drew attention to how far I pulled it and how much time it seemed to take to go back and forth. I then drew attention to pulling it farther (and without letting go), asked, how will the time to go back and forth compare? We discussed this clicker question–> then instead of resolving the issue with debate, we set out to do more mini-experiments. Students of course found that amplitude didn’t effect period, and we had the clicker question debate to make sense of why that answer seemed plausible. I related it back to mathematics—with the math we saw that the Amplitude and Period could be changed independently. With the physical system, too, you could change the amplitude without changing the period.**Direct Instruction on Maximum Speed and Maximum Acceleration**: This is probably the weakest part of the day, but with limited time, I talked about how we had seen with the position vs time graph, the “Amplitude of the Graph” corresponded to the maximum distance that the mass got on either side of equilibrium. On the velocity (and acceleration) graphs, the “Amplitude of the Graph” would correspond to the maximum speed (and maximum acceleration) that the object would achieve. I opened up another Desmos file and walked students through what factors seemed to effect the maximum speed— changing the amplitude or changing the frequency made the maximum speed greater. I related this to their reading, where they had an equation that related maximum speed to amplitude and frequency. This section could have been improved with just one or two clicker questions, where students predict what will happen to the maximum speed when I change Amplitude, and then the frequency. We’d could have then observed on the simulation after having collected our thoughts. I didn’t specifically go through the observations and reasoning about acceleration, but pointed out where in the reading they had seen this.**Problem-solving: Example and Whiteboard.**With some new quantitative relationships in their belts, we needed to do some problem-solving. I don’t always do an example problem, but I did today, because I wanted to model a skill of making good sinusoidal graphs. In the problems, there was not a specific question, but rather information about an oscillation was given, and the task was to draw the position, velocity, and acceleration graphs. This required having to work out period, amplitude, maximum speed, maximum acceleration, whichever wasn’t known. The specific modeling I wanted to do, was identifying “land marks” in the graph. For example, in a position vs time graph, before scribbling a graph, marking some places that you can reason about where the particle will be—half way through the period it will be on the opposite side. Half way through half way, it will be back in equilibrium. Once you’ve identified those landmarks, it’s easier to draw the sinusoidal graph correctly. Anyway, after I modeled solving the problem, students got a problem of their own and worked them out in groups on the whiteboard.

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