# Swinging into Pendulums

## Objective

Students will be able to explore the relationships between pendulum period, mass, string length, and amplitude.

#### Big Idea

Students continue to swing through simple harmonic motion with a pendulum activity today that relates period, mass, string length, & amplitude.

## Context & Equipment Needs

So far in this unit, students have explored simple harmonic motion in mass-spring systems, so today we look at simple harmonic motion in pendulums. After I define characteristics of pendulums (HS-PS3-3), students explore the relationship between the period of a pendulum and its length, mass, and amplitude (SP 1 & 3-6). My hope is that students see evidence of simple harmonic motion in a pendulum system today, and I asses their newly learned knowledge in a one word closure activity.

In preparation for our pendulum activity, I organize and lay out a ring stand, string, a protractor, and various masses for each group. Having these materials ready to go before class allows the lesson to flow without interruption.

## Pendulum Notes

20 minutes

It's time for students to take out their science notebooks and get ready to learn why pendulums are examples of simple harmonic motion. In the notes, I first show students a simple pendulum and its forces, discuss how it relates to simple harmonic motion and mass-spring systems, and describe the period of a pendulum equation. My students are operating under the expectation that they must write down key points from the presentation. This expectation of how to take notes has been outlined and ingrained in their learning since freshman year, but we've practiced it quite a bit throughout earlier lessons in the course as well.

I display the pendulum notes (also available in ppt) to help students understand what they need to write down; I also have a hard copy of the document in my hand. The printed copy includes notes (viewable only when the file is downloaded) that I've written to myself to make sure I accomplish the learning goals as we work through the presentation. The nice thing about having a hard copy in my hand is that if I think of a great side-note or new example, I have the ability to write it down immediately. Having this hard copy also allows me to walk throughout the room as I ask students questions. For example, in the second slide, I ask students "Is energy conserved when a pendulum is in simple harmonic motion?" As we go through the notes, I welcome questions and expect participation from the students.

The presentation ends with a sample problem, so I make sure I use appropriate wait time for students to read the problem and think about their answers. This process usually takes about three minutes, since they have to look at the equation, identify what information they have, and then substitute in the appropriate values. Students have the freedom to write their thoughts or simply sit, think, and substitute values into their calculators. In this example problem, students are usually stumped by the time, since the period is not given, but the frequency. After the few minutes of think time has passed, I ask students to share their solutions. At that point, I then reveal the answers on the slide (it appears with a mouse click) and it's time to move into the next activity.

## Pendulum Lab

25 minutes

During the previous class I assigned partners, so today I allow the students freedom in choosing lab partners. Groups of two to four seem to work best so that all students have an opportunity to be engaged in the activity. As students are organizing themselves into groups, I display the pendulum lab on the front board. The goal of this activity is for students to prove that the period of a pendulum only depends on the length of the string. After everyone is settled, I read the directions to the lab, show students the location of the materials, and go through an example.

The procedure in the lab is purposely vague because I want students to make their own decisions while implementing the science practices. Even though I want students to develop their science-thinking skills, I still make sure to circulate throughout the room and check-in with each group. I want students to use different amplitudes and different masses, along with different string lengths, to justify this conclusion. Finally, the lab also asks students to calculate the pendulum's acceleration due to gravity. This portion of the lab forces students to think about the forces acting on a pendulum in terms of vectors.

I walk around the room offering encouragement as the students think through the design process, and ask questions such as "Are you finding that the amplitude of the string has any impact on the pendulum's period?" or "What type of energy does your pendulum have at that point?" Students understand the expectation that once they have completed collecting the data it's time to move into analyzing their data and writing a conclusion. In fact, it's this analysis section and writing that earns students points for this activity. The AP Physics 1 exam emphasizes students' abilities to design a lab and then draw appropriate conclusions, so this is exactly what I'm looking for when I go through their work.

When there is approximately 10 minutes prior to the end of class (5 minutes left of the time I've allowed for this activity), I ask students to put everything back the way they found it and return to their seats. I also tell them at this point that the lab is due at the start of the next class meeting.

## One Word Closure

5 minutes

To bring closure to our lab today, students need to think of one word that they'd use to describe their thoughts on the lab. After I give them the instructions, students get about 2 minutes to think of their word and then write it on a sheet of paper. As they are thinking about the word, I'm passing out the slips of paper (that I cut before the start of class) and generally checking in with each lab table. This is the students' ticket out the door, so as students leave I ask them to hand me the slip of paper with their word written on as they leave. Some examples of words from this lab include: eh, simple, and phun.

After class is over I go through and read the words students shared. As I do this, I'm making mental notes on the overall tone of their comments. Are students excited and joking? Or, are the students monotone and overwhelmed? Listening to students as they share gives me insight into how the lab went and if I need to make any adjustments. Specifically for this lab, about half the students seemed to think that the lab was average or not special while the other half seemed to enjoy the activity. Because there were no real concerns or negative comments, I can plan on using this activity in the future.