Into the Swing of Things - Lesson
After watching a 1940 film clip of the "Galloping Gertie" bridge collapse and a teacher demo with a simple pendulum, student groups discuss and then research the idea of motion that repeats itself—specifically the concepts of periodic and harmonic motion. They learn the basic properties of this type of motion (period, amplitude, frequency) and how the rearrangement of the simple pendulum equation can be used to solve for gravitational acceleration, pendulum length and gravity.
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Introduction/Motivation

(Be ready to show students a six-minute online video. For a class demonstration, have handy a simple pendulum, such as a ball on a string, to which you are able to vary the length, angle and weight. Also be ready to provide student groups with access to computers with Internet connections for online research.)

In this lesson, you will learn about harmonic motion and its components. Harmonic motion is all around you in the world. It is in the rhythms of nature, how the universe moves, and the mechanical systems that engineers create. Sometimes harmonic motion can cause problems. One famous example is the Tacoma Narrows Bridge, nicknamed "Galloping Gertie." The bridge was designed by structural engineers who did not adequately take into account the role of harmonic motion. Watch this video to see what happened: https://www.youtube.com/watch?v=j-zczJXSxnw.

(After the video, show students a simple pendulum, such as a ball on a string. Demonstrate the motion of the pendulum.) What do you notice about the pendulum and its motion? (As students observe the pendulum, vary different parameters such as length, angle, weight, etc.) How does each change affect the motion of the pendulum?

Next, you will work in groups with the following task: To discuss motion that repeats itself. Think about day/night, clocks, swings, etc. After doing this for a brief time, do some Internet research on the topic of harmonic or periodic motion. What are some examples? How have engineers harnessed this type of motion? What problems can it cause? (Divide the class into small groups and give them time to discuss the topic and conduct some Internet research.) Remember to take notes on what you learn.

(After the allotted time for research and exploration, bring the class together for a discussion to establish a working knowledge of periodic motion. Ask students some questions, such as the following, at a minimum, and get them talking to share what they learned from their research.)

What are some instances of periodic motion in your daily lives? (Possible answers: The seasons, grandfather clocks, playground equipment, tides, vibrating instrument strings, any wave, etc.)

How can you affect the motion of a pendulum? (Answer: Change its length; change its angle.)

What are some basic properties of periodic motion? (Answer: The distance it moves [amplitude]; the time for it to go back to start [period]; the number of cycles for a given time unit [frequency].)

What is period? (Answer: The amount of time it takes for an object experiencing periodic motion to complete one full cycle and return to the same relative position.)

What is amplitude? (Answer: 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.)

What is frequency? (Answer: The number of occurrences of a repeating event per unit time.)

How do engineers exploit periodic motion? (Example answers: The movement in mechanical systems are often repeated [period motion]. Sound and electromagnetic waves serve as communication, etc.)

(Continue by delivering the content in the Lesson Background section.)