Swinging Yo-Yo

What variables affect the period of a pendulum?

If you look around, there are pendulums everywhere. If you’re like a lot of people, the first ones you think of are the ones used to tell time, like in a grandfather clock or a metronome. Pendulums can be completely mesmerizing, just think of a hypnotist with a swinging watch. What makes them both so useful and so hypnotic is the extreme regularity of their swing. But what causes that? What does it depend on? How can the swing be changed?

The simplest pendulum has a string with a mass at the end. In this experiment students will use yo-yos. To start a pendulum swinging, the first thing to do is pull the mass back a little bit. When it's pulled back and held, gravity is pulling directly toward the ground and the string is pulling back toward the pivot point. No matter what happens to the mass of the pendulum throughout the swing, gravity will always be pulling straight toward the ground and the string will keep pulling toward the pivot.

When you let the mass go, gravity pulls it down and the pendulum starts to swing. As it swings it speeds up as gravity makes it accelerate. Because the string is holding it up, it swings in an arc. When it is at the bottom of its swing it is going as fast as it can and gravity is pulling straight down and the string is pulling straight up. As it swings through this point it starts to swing up the other way and gravity is now working to slow it down. When it gets to the top of its swing it has been slowed down to a stop and the whole process repeats in the other direction.

So what affects how fast a pendulum swings? Gravity is one variable. A pendulum on the moon would swing differently than one on earth because the force of gravity would be different.. But, considering you are not taking your class to the moon any time soon, lets concentrate on some other variables. What would happen if you changed the mass at the end of the string? In activity one, we learned that different masses always fall at the same rate. Because of this factor, changing of the pendulum’s mass will not change how fast it swings. What happens if you start it out with a greater amplitude? It will still take the same time to get through one swing, it will just be going faster at the bottom of the swing. It had more time to speed up as it was swinging, so it is going faster, but because it is going faster, it covers a larger distance in the same amount of time.

The last easy thing to change is the length of the string. This is the only variable (that we can easily change) that affects the period of a pendulum. The longer the string, the more time it takes to go through one swing. So if you want to set your grandfather clock, the only thing you need to change is the length from the pivot point to the mass. If you’ve ever played the piano, you will remember that this is how a metronome is set, by sliding the mass. Pendulum motion is a neat thing to have your students explore in a more free form way. There are only really three variables they can change, mass, length and starting amplitude, and one variable they can measure, the period. In addition to teaching students about pendulums, this activity has them design their own experiment and learn that it’s only useful to change one variable at a time, that they should do repeated trials and that there are many different ways to represent results, some more useful than others.

Make sure to give your students the guidance they need and make sure that different groups are changing different variables. With limited class time, all students will be able to see what happens when each variable is changed.

• Real world connections -
  • Explain with a CER paragraph what is going on with the pendulums in the original video we watched/
  • Using what you learned about how different variables affect how long it takes a pendulum to swing, how can you change the tempo on a traditional metronome? Helpful Resource
• Suggestions for drawing, illustrating, presenting content in creative ways
  • Consider cross curricular study with art classes by having students create a “pendulum painting” and explore the visual patterns of this motion
• Engineering and design challenges connected to the content
  • Design a structure that could use the movement of a pendulum in it’s design
    • What problem can you solve using pendulum movement?
    • How would this structure help people or the Earth in any way (be creative)

• 4-PS4-1
  Develop a model of waves to describe patterns in terms of amplitude and wavelength and that waves can cause objects to move.
• MS-PS4-1
  Use mathematical representations to describe a simple model for waves that includes how the amplitude of a wave is related to the energy in a wave.
• MS-PS4-3
  Integrate qualitative scientific and technical information to support the claim that digitized signals are a more reliable way to encode and transmit information than analog signals.

Credits