Pendulum Activity

I use this activity on the first day of school. It serves many purposes for me, including introducing the students to me and their classmates, demonstrating how hands-on activities will be used in the classroom, evaluating the students’ problem solving and graphing abilities, establishing the concept of pattern analysis, and addressing measurement skills.

Pendulum Activity – Teacher’s Notes

1) As students arrive, they are given a piece of string (0.25m-1.0m) and a washer. They are asked to tie the washer to the string.

2) As a class, brainstorm different values that can be measured with regards to the string and the washer system. Students should identify the following: length of string, volume of washer and string, mass of washer and string, time of swing (period of pendulum), angle of release, and length of string to center of washer.

3) Students are asked to measure only the period of the pendulum. Before they begin the experiment, the class should discuss what should be done to get “good” data. Students might identify that the mass of the washer should be the same for all students, the volume of the washer should be the same for all students, the angle of release should be the same (actually the volume, mass and angle do not need to be consistent among groups because the period is independent of these values assuming negligible air resistance and small release angle, but might be good to enforce so they will not see that as a possible source of error), the number of periods timed should be greater than 1 (in fact, they should take time for at least 5 back and forth swings and then divide their total time by five), the number of trials should be greater than 1 (4-6 trials is recommended), and the string should be held at its tip.

4)

tacks

While the students measure the period of their string/washer system, the teacher should write a time line along the top of the blackboard.

5) Once the students have finished their measurement of the period, they are asked to tack their washers and strings to the tack-strip above the blackboard at the location that corresponds with the time of the period.

6) Once the students have all tacked their strings to the board, the class discusses the trend(s) seen in this experiment. It becomes evident that the longer the string, the longer the period.

7) The teacher then brings out a 6 meter long string attached to a washer and asks the students to predict the period of this string. The students will most likely assume a linear relationship at this point – they will measure the lengths of the strings and record the time associated for that length. This data will be plotted on graph paper and the students will extrapolate their best estimate of the period value. If they assume a linear relationship, they will get a value of about 12-13 seconds for the period.

8) The class then measures the period of the 6m length of string attached to the washer. The students then see that there is not a linear relationship (or at least their predicted period is wrong). Therefore, the periods of lengths of 2, 4, and 5 meters are also measured.

9) As a class, the students and teacher plot data points (for time and length) corresponding to 1, 2, 4, 5, and 6 meters. At this point, the graph can be a quick sketch. Based on the sketch, the students should predict the period of a 3 meter long pendulum by referring to the graph.

10) As homework, the students are asked to input the data points (for time and length) corresponding to 1, 2, 3, 4, 5 and 6 meters into a table in their graphing calculator. Students can use this data in a scatter plot to try to predict the equation of the period of a pendulum – they can then double check themselves using the power regression feature on the calculator.

The expected equation:

period in seconds = 2 p ( length in meters / 9.8 )^½

The expected data: