The Period of a Pendulum (Part 2)

In Part 1, you built a pendulum and tested it against a model for $\theta \leq 10^{\circ}$. In this second part, you will re-create your pendulum and collect data over a larger range of angles.

As with the first part, today you will be exploring experiment design, repeatability, systematic biases, statistical distributions, and model-testing.

Part 2: Revisiting your pendulum for $\theta > 10^{\circ}$

In part two, you will continue working on your pendulum, and you will extend your measurements to angles greater than 10 degrees.

Lab notebook

Open up your lab notebook from last week.

  • You will continue writing in this document. Do not start a new Google Doc (unless you are part of a new group that did not complete the lab last week)!
  • Make a clear mark to indicate where Part 1 notes end and Part 2 notes begin. (You may want to copy the title, date, and student name block and paste it at the start of Part 2.)
  • For Part 2 of the experiment, we won't provide prompts… use your judgement to decide what to record in the lab notebook. Remember this is supposed to be a complete picture of what you did… include notes on process, data, analysis, and thoughts/reactions. Don't erase; only add.

Rebuilding/improving your pendulum

You will need to rebuild your pendulum… did you keep good enough notes from Part 1?

  • It's OK if your group wants to change something about the pendulum or measurement technique. You've had a week to think about the experiment… maybe you've got some new ideas!

After about 15 minutes, your TA will ask groups to talk to each other to learn more about techniques that others in the class are using.

  • Again, it's OK if your group wants to change something after talking to other groups. Learn from each other!

Collecting more data

Now, let's test the model at larger angles. Does the model from last lab still hold? How can we tell when we have agreement? When do we have disagreement? When is it inconclusive?

As with last week, we again provide a Google Colab notebook to help you do calculations and visualize your data.

Remember that the TA will come around to talk to each group and to check lab notebooks, so remember to record and think about your data as you go! Remember to record you data in your lab notebook directly – not just in the Google Colab notebook. (It might crash!)

Speak with your TA as you progress. They will help you determine when you've explored the system fully enough.

Submit your lab notebook

Make sure to submit your lab notebook by the end of the period. Download a copy of your notebook in PDF format and upload it to the appropriate spot on Canvas. Only one member of the group needs to submit to Canvas, but make sure everyone's name is on the document!

Don't forget to log out of both Google and Canvas, and to close all browser windows before leaving!

Post-lab assignment


Answer the questions/prompts below in a new document (not your lab notebook) and submit that as a PDF to the appropriate assignment on Canvas when you are done. You should write the answers to these questions by yourself (not in a group), though you are welcome to talk to your group mates to ask questions or to discuss.

Conclusions

As we did last week, let us again practice drawing conclusions.

The conclusion is your interpretation and discussion of your data.

  • What do your data tell you?
  • How do your data match the model (or models) you were comparing against, or to your expectations in general? (Sometimes this means using the $t^{\prime}$ test, but other times it means making qualitative comparisons.)
  • Were you able to estimate uncertainties well, or do you see room to make changes or improvements in the technique?
  • Do your results lead to new questions?
  • Can you think of other ways to extend or improve the experiment?

In about one or two paragraphs, draw conclusions from the pendulum data you collected today. Address both the qualitative and quantitative aspects of the experiment and feel free to use plots, tables or anything else from your notebook to support your words. Don't include throw-away statements like “Looks good” or “Agrees pretty well”; instead, try to be precise.

Questions

Consider the following questions:

  1. Early in the lab, you had a discussion with a neighboring group (or groups) to compare your pendulums and measurement technique(s). What did you learn from the other group(s)? Did any of your measurement techniques or ideas change after speaking with the other group(s)? If so, how and why?
  2. At the start of Part 1, we provided you the model against which you were going to compare your data ($T = \sqrt{L/g}$) and you therefore were collecting data with an expected outcome in mind.
    1. How might having an expected outcome in mind before starting an experiment be useful or helpful?
    2. How might having an expected outcome in mind before starting an experiment be unproductive or unhelpful?
    3. Assuming we can never remove all expectations or predictions, what are some strategies we can take in the lab to mitigate potential issues? Provide actionable strategies (not just “don't be biased”).

REMINDER: Your post-lab assignment is due 24 hours after your lab concludes. Submit a single PDF on Canvas.