students should know the relationship between period and frequency, the linearized and non-linearized differential equations of motion for a pendulum, and what the assumptions mean that could give discrepancies between phenomenon in real life and our theory.

MATLAB helps visualize, plot, and compare the different behavior of the system (measured, linearized, non-linearized), and help provide understanding of what the trade-offs are with assumptions and simplifying equations to model real-life scenarios.

The most important learning is that some of the theory we learn in class rely on assumptions and simplifications that are not necessarily true for real-life scenarios, so that they can see when those assumptions fail. students also have the ability to see when those assumptions do hold true as well. I think this activity calls upon all of the higher-order thinking skills mentioned above.

Students also need to have skills in technical writing, field measurements (and corresponding error and uncertainties), and more.

This activity could easily be done as part of class, or as a take-home project like I had implemented. The time it takes to do the activity depends on the student and which pendulum they decide to model and measure. I implemented this in ME350, which is a junior level class that is required for the students in mechanical, aerospace, acoustical, and robotics engineering, and those getting the mechanical engineering minor.

Students should be familiar with plotting sine waves, solving differential equations, and plotting the behavior over time. Students should know how to write reports and explain their findings. Students should be able to take measurements of the period of the pendulum, and calculate the natural frequency.

I have it so that it's a take-home "quiz," a easier project that can help improve their overall quiz score. However, this activity can be easily modified to either be a simple in-class exercise, a lab, or a multi-day lab.

The objective of this quiz is to find a simple harmonic motion system in your daily life, take measurements of its natural frequency, and compare with the calculated natural frequency.

Please see attached for instructions:

I also ask students to provide me a .pdf of the report, .xlsx of their measurements, and .m of their MATLAB file.