Effect of Length, Mass, and the Arc on the Frequency of a Pendulum

Researched by Cory C.
2003-04



PURPOSE

In phase 1 the purpose was to determine the effect of the arc (angle of the swing) on the frequency of a pendulum.

In phase 2 the purpose of this experiment was to determine the effect of length on the frequency of a pendulum.  

In phase 3 the purpose of the experiment was to determine the effect of mass (weight) on the frequency of a pendulum.

I became interested in this idea when I learned about pendulums from a television show.

The information gained from this experiment will help people who buy old fashion pendulum clocks because they may swing at different speeds which would make them run too fast or too slow.
 
 


HYPOTHESIS

My hypothesis for phase 1 was that the larger the angle of the swing (arc) of the pendulum, the slower the frequency of the pendulum.

My hypothesis for phase 2 was that the longer the pendulum, the slower the frequency of the pendulum.

My hypothesis for phase 3 was that the heavier the pendulum, the slower the frequency of the pendulum.

I based my hypothesis for phase 1 on my observation of playground swings. The longer the size of the arc, the slower it takes for a full swing.

I based my hypothesis for phase 2 on my observation of playground swings.   The longer the swing is the slower you appear to swing.

I based my hypothesis for phase 3 on my observation of playground swings. The heavier the person on the swing the slower you appear to swing.

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EXPERIMENT DESIGN

The constants in this study were: 

  •  Materials of a pendulum 
  • Support line 
  • Anchor point
  • A stopwatch 
  • The length of the pendulum stays the same
  • The weight of the pendulums stays the same
  • The humidity stays the same
  • The wind in the room must stay the same.
The manipulated variable for phase 1 was the arc (swing angle) of the pendulum.
The manipulated variable for phase 2 was the length of the pendulum.
The manipulated variable for phase 3 was the mass of the pendulum.

The responding variables were the frequency of the pendulum in swings per minute.

To measure the responding variable I counted the number of full swings in 30 seconds and multiplied that by 2.

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MATERIALS


Quantity Item Description
1 Tape
1 Pencil
1 Calculator
1 Protractor
1 Stopwatch
1 Metric Ruler
1 String (about 200 cm)
1 A friend or family member
4 Weights
1 Long wooden block

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PROCEDURES

1. Find a place where it is possible to set up a pendulum (best place is in the middle of a room or anywhere that the pendulum won’t hit anything).
2. Set up the pendulum.
a. First get a long wooden board with a ring (eyebolt ) on the bottom of it and a nail on top.
b. First tie the string to one of the weights (washers).
c. Slide the string through the ring and up tie it around the nail on the top of the wooden board.
3. Pull back the weight and let go of it so that it swings freely back and forth, not in a loop. Practice this a few times so that when you do the test you know how far up you pull the weight before you let it swing.
4. In phase 1 tie two of the weights to one of the ends of the string and slide the string through the ring and tie the other end of the string to the nail on the top of the wooden block so that the length between the weight and the ring is 100 cm.
5. Phase 1 should be done with 2 washers and 100 cm of length.
6. For phase 1 get a protractor and have the helper hold it up at the top of the pendulum, and make sure the pendulum is exactly 15 degrees angles from vertical when released.  
7. Pull back the weights tied to the string and ask a helper to say, “go” and have them start the stopwatch and let go of the weight.
8. Once you let go of the weight start counting the number of full swings 
  (periods) until the helper says, “stop”.  
9. Repeat step 6- 8 for a total of 5 times.
10. Repeat steps 6-9 for several other starting angles (30 degrees, 45 degrees, 60 degrees, and 75 degrees from vertical).
11. Record your data on “Data Table A: Arc Variable. ” To find the results for 1 minute multiply the results you got for 30 seconds by 2.
12. Phase 2 should be done with 2 washers at 45 degrees.
13. In phase 2 tie one of the weights to one of the ends of the string and slide the string through the ring stand and tie the other end of the string to the nail on the top of the wooden block so that the length between the weight and the ring stand.
14. Repeat steps 5- 8 with different lengths of the strings by pulling the string through the ring stand tying it around the nail (20 cm, 40 cm, 60 cm, 80cm).
15. Record your data on “Data Table B: String Length Variable. ”  To find the results for 1 minute multiply the results you got for 30 seconds by 2.
16. Phase 3 should be done with 100 cm of string at 45 degrees from vertical.
17. In phase 3 just repeat steps 7-9 with different weights (15 g, 30g, 45g, 60g, and 75g).
18. Record your data on “Data Table C: Weight Variable. ” To find the results for 1 minute multiply the results you got for 30 seconds by 2.

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RESULTS

The purpose for phase 1 was to determine the effect of the arc (angle of the swing) on the frequency of a pendulum.
The results of the experiment for phase 1 was strange because unlike the others, it doesn’t go up or down, it goes up then down. 30 ° had 28. 6 periods, 60° had 28. 8 periods, 90° had 30. 8 periods, 120° had 28. 4 periods, and 150° had 26. 6 periods (nothing like the others).

The purpose for phase 2 was to determine the effect of length on the frequency of a pendulum.  
The results of the experiment for phase 2 was the longer your string is the slower it goes and vice- versa. In my research 20 cm had a lot more periods than 100 cm. The average amount of periods for 20 cm is 63. 8 and the average periods for 100 cm is 38. 8 (major difference).

The purpose for phase 3 was to determine the effect of weight (mass) on the frequency of a pendulum.  
The results of the experiment for phase 3 was that the heavier the pendulum the less swings there were and vice- versa. In my research 15 grams had a little bit more of periods than 75 grams. The average amount of periods for 15 grams is 31 and the average for 75 is 29. 4 (small difference).

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See my data table and graphs.
 
 



CONCLUSION

My hypothesis for phase 1 was that the larger the angle of the swing (arc) of the pendulum, the slower the frequency of the pendulum.

The results indicate that this hypothesis should be rejected because there was almost no difference due to angle.
My hypothesis for phase 2 was that the longer the pendulum, the slower the frequency of the pendulum.

The results indicate that this hypothesis should be accepted because at first the shorter string had a lot of swings and the longer I made the string, the fewer swings there were.

My hypothesis for phase 3 was that the heavier the pendulum, the slower the frequency of the pendulum.

The results indicate that this hypothesis should be rejected because there was almost no difference due to mass.

Because of the results of this experiment, I wonder if these results would also apply to double or triple pendulums.

If I were to conduct this project again I would try to conduct the experiments more than five times. I might also try to do more than five different treatments (angle for phase 1, length for phase 2, and mass for phase 3).

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RESEARCH REPORT






Introduction
A pendulum is a weight that is hanging from a fixed point by a string or wire, so that it can swing freely back and forth caused by the gravitational pull.
Galileo Galilei was the person who discovered the pendulum when he was watching a chandelier swing in a cathedral in Pisa.  
Christiaan Huygens made the first pendulum.
Leon Foucault wanted to prove that the Earth rotates, so he built a huge pendulum.  
 
 

Types of Pendulums
There are quite a few types of pendulums. One of the most common pendulums is the clock pendulum. This is a type of pendulum is the single pendulum. A single pendulum swings forward and backward from a fixed point.

There are 4 types of pendulums that most people probably haven’t heard about. They are double pendulums, triple pendulums, quadruple pendulums, and quintuple pendulums. Double pendulums are single pendulums attached to another. Triple pendulums are double pendulums with another pendulum attached to it. Quadruple pendulums are triple pendulums with another pendulum attached to it. Quintuple pendulums are quadruple pendulums with another pendulum attached to it.

There are many more pendulums.  
 
 

Frequency of a Pendulum
The frequency of a pendulum is how fast it moves back and forth.   The pendulum’s speed is usually faster the shorter the string of the pendulum is. The mass of the pendulum doesn’t have that big of an effect on the pendulum’s frequency. It doesn’t matter that much about the mass of the pendulum, so if you get different size weights you should get close to the same answers (usually). The place that you start your pendulum from does matter but not as much as the length.
 
 

Length of a Pendulum
The length of a pendulum is how long the string or wire is from its fulcrum to center of the weight. According to my research the longer your string the slower it goes and vice- versa.  
The length of a pendulum makes a huge difference for the pendulum.   According to my research, if you use length you should probably use one long size and one short size (if not more than one). If you do several types of tests ( such as length, weight, and the arc) length will most likely have the biggest effect.
 
 

Summary
One of the only things that pendulums are usually used for are for clock pendulums. So people have largely stopped using pendulums.  

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BIBLIOGRAPHY

Chalupnik, James D. "Pendulums," World Book Encyclopedia. 2002.

“Clock. ” The Hutchinson Dictionary of Science. 1998.

“Clocks and Watches. ” Young Students Learning Library. 1996.

“Galileo properly Galileo Galilei (1564-1643). ” 
The Hutchinson Dictionary of Scientific Biography. 1998.  

“Pendulum. ” Young Students Learning Library. 1996.

“Pendulum. ” November 20, 2003. http://www. fofweb. com 

“Pendulums: Simple and Otherwise. ” December 3, 2003 www. delphiforfun. org/programs/pendulum.htm 

“Watch and Clock. ” Britannica Intermediate Encyclopedia. October 29, 2003. Elibrary.

“Zoom Pendulum. ” November 20, 2003 http://www. pbskids. org 

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ACKNOWLEDGEMENTS

 I would like to thank the following people for helping make my project possible:

  •  My parents for encouraging me to keep doing my best and getting me materials.
  • Mr. Newkirk for helping me whenever he could and having after school classes.
  • Mrs. Helms for helping me when she could or when Mr. Newkirk was busy, and for getting me information.


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