SummaryStudents investigate the motion of a simple pendulum through direct observation and data collection using Android® devices. First, student groups create pendulums that hang from the classroom ceiling, using Android smartphones or tablets as the bobs, taking advantage of their built-in accelerometers. With the Android devices loaded with the (provided) AccelDataCapture app, groups explore the periodic motion of the pendulums, changing variables (amplitude, mass, length) to see what happens, by visual observation and via the app-generated graphs. Then teams conduct formal experiments to alter one variable while keeping all other parameters constant, performing numerous trials, identifying independent/dependent variables, collecting data and using the simple pendulum equation. Through these experiments, students investigate how pendulums move and the changing forces they experience, better understanding the relationship between a pendulum's motion and its amplitude, length and mass. They analyze the data, either on paper or by importing into a spreadsheet application. As an extension, students may also develop their own algorithms in a provided App Inventor framework in order to automatically note the time of each period.
Harmonic motion is prevalent in the repetitive (periodic) motion found in the rhythms of nature on Earth and in the universe, as well as human-made devices such as watches, clocks, toys and uncountable mechanical systems. Engineers incorporate regular periodic motion into some designs, and must understand and adapt other designs to fit the periodic motion present around them.
- Students should know basic information about pendulums and how they functions from different perspectives, as provided in the associated lesson, Into the Swing of Things. As necessary, refer to the lesson for detailed information about periodic motion to help students with this activity.
- Students who are familiar with the App Inventor platform may want to modify the provided application to collect data specific to their experiments and/or automate the pendulum period calculation.
- Students with an understanding of trigonometric functions may have a more meaningful learning experience as trig functions as can be seen in the acceleration graphs/data for the individual axes.
After this activity, students should be able to:
- Explain the basic properties of periodic motion (specifically, in a pendulum).
- Analyze Android app-generated graphs representing periodic motion.
- Use pendulum equations to solve problems related to pendulum motion.
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within type by subtype, then by grade, etc.
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
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Each group needs:
- supplies for pendulum construction and attachment to ceiling, such as string, tape, cable ties, rubber bands, cardboard, binder clips
- ceiling, from which to hang a pendulum
- ruler, for measuring pendulum length
- scale, for measuring the pendulum bob mass
- protractor, for measuring the pendulum angle/amplitude
- (optional) balance weights, to adjust the pendulum mass
- AccelDataCapture.apk, an Android application
- Android device, such as a smartphone or tablet; must be an Android 2.2 or higher to use the AccelDataCapture.apk file
- AccelDataCapture Documentation, one per group
- Data Collection Sheet 1, Data Collection Sheet 2 and Post-Activity Quiz, one each per student
- (optional) computers with spreadsheet software
- (optional) computers capable of App Inventor programming
Harmonic motion is evident everywhere in our world. Engineers often take advantage of periodic motion to make systems functions. At other times, engineers must avoid setting up situations in which harmonic motion can occur and might be problematic.
For instance, some mechanical engineers work with mechanical systems that involve harmonic (periodic) motion, such as the internal combustion engine. This system depends upon very predictable positions at given times for its various components, which all function in a period of rotation for the crankshaft. When the engine is in operation, its components must be carefully timed to fit the periodic motion that is occurring.
On the other hand, structural engineers are very aware not to inadvertently set up harmonic motion on suspension bridges. An engineer's focus is to cancel forces so that periodic motion does not build up. As an example, recall the video clip you watched in the associated lesson about the Tacoma Narrows Bridge collapse in 1940!
AccelDataCapture: An Android application created by Douglas Bertelsen for the University of Nebraska at Omaha's 2013 NSF Research Experience for Teachers grant and provided as an attachment to this activity.
accelerometer: A sensor that measures the acceleration of an object
amplitude: A periodic variable that is a measure of change over a single period. Typically, it is measured from an object's equilibrium point to its most extreme value.
App Inventor: An open-source (free) web application for creating software applications for the Android operating system. See http://appinventor.mit.edu/explore/.
harmonic motion: A type of periodic motion in which the restoring force is directly proportional to the displacement.
pendulum: A weight suspended from a pivot point such that it can swing freely.
period: The amount time it takes for an object experiencing periodic motion to complete one full cycle and return to the same relative position.
periodic motion: Any motion that repeats over and over again with the same time required for each recurrence.
In this activity, students explore one small aspect of harmonic motion—pendulums. Using Android devices with built-in internal sensors (specifically accelerometers) as pendulum bobs, student groups experiment and collect data about how pendulums work and then modify certain aspects of their pendulums to see some of the mathematical relationships present in the pendulums' motion.
Before the Activity
- Review the Typical Pendulum Setup to see photos of two example pendulums created by students and two ways they were attached to ceilings. Decide what construction materials to provide for students and determine the best way to hang the Android pendulums from your classroom ceiling. Test this setup.
- Decide whether to have students conduct the activity individually or in small groups, depending on the number of available Android devices.
- Review the three suggested experiments described below; decide if you want to create different or additional experiments for students to conduct.
- Gather materials for the activity.
- Make copies of the Data Collection Sheet 1, Data Collection Sheet 2 and Post- Activity Quiz, one each per student, and the AccelDataCapture Documentation, one per group.
- Load the Android application, AccelDataCapture.apk, onto each Android device. Instructions for "sideloading" an application are readily available on the Internet (device differences may exist) and involve the following basic steps. No additional installer app is necessary!
- Put the app on the device via USB or download from the web.
- In the device settings, check "Allow installation of non-market applications."
- Select the .apk file to be installed and approve the app permissions.
- Note: The source code for the AccelDataCapture.apk app is provided in the AccelDataCapture folder in the AccelDataCapture zip file (in the Attachments section). While it is not needed for this activity, it may be useful for teachers or students who want to modify the application as an activity extension.)
With the Students
- Review the concepts students learned in the associated lesson by asking them a few questions, as described in the Assessment section.
- Present to the class the Introduction/Motivation content.
- Provide an overview of the activity: To investigate how pendulums move and the changing forces on pendulums by using the accelerometers in Android devices.
- Divide the class into small groups. Hand out the pendulum construction supplies, Android devices and copies of the data collection sheets and the app documentation sheet.
- Provide some advice and/or examples for how to create pendulums with the provided supplies and Android devices. Student groups can use any of the provided materials to create their pendulums. Remind students to take care with the (expensive and delicate) devices and make sure they are securely attached as the pendulum mass/bob before letting them swing.
- Show how you would like teams to attach their pendulums to the classroom ceiling, based on your advance testing of the best setup for your classroom.
- Explain that groups will be using the AccelDataCapture app on their Android devices. The basic instructions for the AccelDataCapture app are available at the "info" screen in the app and on the documentation sheet.
- Next, give the teams some time to create their pendulums. Do not permit them to swing the pendulums in full circles; instead, direct them to swing them like grandfather clock pendulums.
- Once groups have created their pendulums, have them gently push them to observe their motion.
- Pendulum Observations & Exploration: Have students conduct basic experimentation by changing one variable at a time (such as amplitude, mass and length) and recording their qualitative observations of the pendulum on the first data collection sheet using direct visual observations of the pendulum as well as the graphs generated by the AccelDataCapture app.
- Pendulum Experiments: Next, have each group conduct a specific experiment in which they use the AccelDataCapture app to understand the relationship of amplitude, length, mass of a pendulum and its periodic motion. Have groups choose (or assign) a particular experiment to run with the pendulum setup. Recommended experiments include:
Experiment 1: Vary the length, while keeping all other parameters (mass and amplitude) constant
- A range of four evenly distributed lengths between 0.2 and 1 meter is sufficient. If possible, extend the lengths to 2 meters for best results.
- The best measurements are from the top of the pendulum to the center of gravity. This is simplified with a sphere in many experiments. Suggest students try to locate the center of gravity to improve their results.
Experiment 2: Vary the mass, while keeping all other parameters (length and amplitude) constant
- Attach weights from balances to vary the mass; however, varying mass has little effect on the period, as it is not a term in the equation.
- Expect weights up to double the starting weight to have minimal effect on the period. Most of this is either due to changing the center of gravity of the device or creating a better mass/drag ratio.
Experiment 3: Vary the amplitude (starting angle), while keeping all other parameters (length and mass) constant
- Use a protractor to measure the starting angle at the top of the pendulum.
- Because of the small-angle approximation of the sine function, angles under about 30° result in only a 2% variation.
- A range of four angles between 5-20° gives good results.
- Direct students to record their experiment data on the second data sheet, personalizing the data collection table with their experiment details, and using the AccelDataCapture app and visual observations.
- Have each group choose at least five variations of its independent variable (length, angle/amplitude, mass, etc.) to test in order to determine the resulting period of the pendulum's motion.
- It is recommended to conduct at least two or three trials for each variation and average together the resulting periods to improve accuracy.
- Make sure students identify the period of the pendulum's motion as the dependent variable for each of the recommended experiments. Help guide them to this if they have trouble identifying the dependent variable based on varying one of the independent variables (length, mass, amplitude).
- One common pitfall is to count a swing in one direction as a period rather than a full swing involving a return to the starting point.
- Have students record the data directly off of the Android device or export it using the save function of AccelDataCapture and import it into a spreadsheet program for graphing or data analysis such as best-fit, error or standard deviation.
- If time permits, have each group choose another experiment by selecting a different independent variable to vary and repeat step 12 for a second experiment.
- Conclude by administering the post-activity quiz, as described in the Assessment section.
Android devices are expensive and somewhat delicate. Remind students to take great care to make sure their devices are securely attached as the pendulum bobs before attempting to swing them. And then, never swing them in full circles; instead, swing them like clock pendulums.
Watch that students do not count a swing in one direction as a period; rather, a period is a "full" swing involving a return to the starting point.
Watch that app navigation on the Android device is still possible with whatever methods students use to attach their devices as the pendulum bobs.
Concept Review: Ask students to recall what they learned in the associated lesson about pendulums and periodic motion. Example review questions:
- What are the elements of a simple pendulum that are included in the simple pendulum with small-angle approximation? (Answer: Length, gravitational acceleration and the period of the pendulum's motion.)
- From your everyday experiences, what are some examples of periodic motion? (Example answers: Clocks, rocking chairs, vibrating instrument strings, water wave, motors, ocean tides, the movement of the Sun, etc.)
Activity Embedded Assessment
Observations: As students are engaged in the lesson ask yourself these (or similar) questions to make sure they understand the relationship between a pendulum's motion and its amplitude, length and mass:
- Do students understand what happens to the period of the pendulum as the amplitude (starting angle) is changed? (Answer: The period of the pendulum is largely unaffected with smaller angles.)
- Do students understand what happens to the period of the pendulum as the length increases? (Answer: The period of the pendulum increases as the length increases.)
- Can student explain what happens if the pendulum mass changes? (Answer: No change in period; the mass is not part of the pendulum equation.)
Post-Activity Quiz: At activity end, administer the Post-Activity Quiz, which asks students to use the simple pendulum equation to solve problems related to the periodic motion of planets. Review their answers to gauge their understanding of the concepts. The answers are provided on the Post- Activity Quiz Answer Key.
Students who are familiar with the App Inventor platform may want to modify the AccelDataCapture app to collect data specific to their experiments and/or to automate the pendulum period calculation. To modify the app, its source code is provided in the AccelDataCapture folder in the AccelDataCapture zip file (in the Attachments section).
Copyright© 2014 by Regents of the University of Colorado; original © 2013 Board of Regents, University of Nebraska
Supporting ProgramIMPART RET Program, College of Information Science & Technology, University of Nebraska-Omaha
The contents of this digital library curriculum were developed as a part of the RET in Engineering and Computer Science Site on Infusing Mobile Platform Applied Research into Teaching (IMPART) Program at the University of Nebraska-Omaha under National Science Foundation RET grant number CNS 1201136. However, these contents do not necessarily represent the policies of the National Science Foundation, and you should not assume endorsement by the federal government.
Last modified: August 29, 2017