Paper Clip Pendulums
A quick and easy activity for teaching data analysis.

vibrations, periods, data analysis

1 box of standard paper clips, stopwatch
1. Bend one paper clip into a hook. This paper clip will not be counted and will be referred to as “the hook”.
2. Clip 10 paper clips end-to-end from the hook.
3. Holding only the hook, hang the paper clips vertically and pull the bottom one back so it makes about a 30o angle with the vertical.
4. Release and let the paper clip pendulum swing freely.
5. Time five periods of the paper clip. A period consists of the time it takes for the paper clips to swing back and forth once.
6. Find the average period by dividing the total time in seconds by 5.
7. Repeat steps 1-6 but use 15, 20, and 25 paper clips.

Results and Discussion
  • Record the final data in a table with two columns; the first should be “Number of Paper Clips” and the second should be “Average Period (seconds)”.
  • Graph the data using an appropriate graph type such as a scatter plot. Label the axes of the graph and include units if applicable.
  • Answer the following questions:
    • What happens to the period of a pendulum as the length increases?
    • Describe the shape of the graph and make a prediction about what the period would be if you had timed 30 paper clips.
A pendulum is an example of a vibration with a regular, consistent motion. The period of a pendulum depends on its length. The longer a pendulum the longer its period, and the shorter a pendulum the shorter its period. More exactly, the period of pendulum is proportional to the square root of the length. For a standard paper clip a typical table and graph of data are shown below.

Figure 39: A 10 clip paper-clip pendulum with the top pendulum acting as a handle

Figure 40: Typical student data showing average period versus number of paper clips.

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