Changing the Period of a Pendulum
Imagine that your plane has crash landed on a desert island. You don’t have a working clock, so you can’t tell when afternoon teatime is! You set out to make yourself a clock. The plane was carrying a book on whittling wood into gears as well as a book that describes the construction of pendulum clocks—how convenient! However, the pages that describe how to make the correct pendulum are missing. You don’t know how long or heavy it needs to be or how hard it needs to swing to tell time correctly! You’ll have to figure that part out on your own.
Problem: How does a pendulum work?
- Weights (Metal washers are perfect for this)
- Plastic Straw
- Pen & Paper
- Tie one weight onto the thread.
- Thread the thread through the straw and tape the straw to your table so that about half an inch of the straw hangs over the table’s edge.
- Tape the non-weighted end of the thread to the table so that the length from the end of the straw to the middle of your weight is 4 inches.
- Let the pendulum settle so that it is not moving.
- Pull it to the side about one inch and let it go, gently. If the pendulum bounces or vibrates, allow it to settle and try again. Your goal is to make the pendulum swing in a steady arc.
- As you let it go, start your stopwatch and count the number of times it swings from its starting point to the other side and back until you count 10 swings. Stop your stopwatch. Record both the time it took for the pendulum to complete 10 swings and the length of string. Repeat this three times and average together the data you collect from all three trials. The ratio of swings to time is called the period of your pendulum.
- Adjust the length of the pendulum from 4 inches to 3 inches. Repeat steps 4-6. How do you think the changed length will affect the pendulum’s behavior? Why?
- Double the length of the pendulum to 6 inches and repeat steps 5 and 6. Do you think the added length will change anything? Why?
- Repeat steps 4-8, but pull the pendulum 3 inches to the side as opposed to 1 inch before letting it go. How do you think this will affect the pendulum’s behavior? Why?
- Now experiment with increasing the weight of your pendulum’s bob. If you’re using washers, then simply tie a second washer to the end of your string. Repeat steps 4-8 with your larger weight. How do you think using a heavier weight might affect the behavior of the pendulum? Why?
Only the length of the string has any effect on changing the period of a pendulum. Neither changing how heavy it the bob is nor how far to the side you pull it before letting it swing (unless you pulled it very far to the side) will change the time it takes the pendulum to complete a swing from one side to the other. The pendulum’s period remains constant in both cases. A heavier pendulum bob will help the pendulum swing for longer, however.
These characteristics make the pendulum a great tool for keeping time. An advantage of longer pendulums is that they can swing in smaller arcs while travelling the same distance as shorter pendulums. This helps limit some errors due to pendulum behavior not perfectly matching the math you need to keep time.
Pendulums behave according to the phenomenon of a restoring force, a force that pushes something back to its central position. Whenever the pendulum isn’t hanging straight down, the tension from the thread pulls it back to this central position. How hard the thread pulls directly depends on how far away the pendulum is from its center, which is exactly the type of relationship necessary for a machine to be an oscillator—something that consistently moves back and forth a specific number of times per second. All clocks use oscillators, and pendulums were the best oscillators available in the 19th century.
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