Introduction: (Initial Observation)
Pendulum or other swinging objects can be found everywhere. Pendulum is one of the first known timing devices and is the fundamental technology behind wall clocks. Galileo used pendulums extensively in his experiments. You can still purchase decorative clocks with pendulum. The physics of pendulum is used almost in any device that has a swinging part.
In this project you will design an experiment in order to find out how you can decrease or increase the period of a pendulum.
Information Gathering:
Find out about Pendulums. Read books, magazines or ask professionals who might know in order to learn about the factors that affect a pendulum period. Keep track of where you got your information from.
following are samples of information that you may find.
Galileo’s Pendulum Experiments
Galileo used pendulums extensively in his experiments. Early in his career, he researched the characteristics of their motion. After investigating their behavior, he was able to use them as time measurement devices in later experiments.
Galileo discusses some of the major points he discovered about pendulums. Follow the links to jump to an experimental evaluation of the claim.
- Pendulums nearly return to their release heights.
- All pendulums eventually come to rest with the lighter ones coming to rest faster.
- The period is independent of the bob weight.
- The period is independent of the amplitude.
- The square of the period varies directly with the length.
Galileo also performed experiments to examine the nature of collisions in which he used pendulums, but these experiments appear to have provided less insight and to have been less conclusive than the other experiments. These collision experiments were not repeated or evaluated.
We attempted to reproduce Galileo’s findings on these main points and verify his claims. Galileo’s techniques had to be modified in several ways to be practical for our resources. For one experiment in Two New Sciences, string lengths of four or five yards are suggested. For these experiments, string lengths of 24.0 cm to 99.4 cm were used. The experiments also used lead and cork balls. For these experiments, egg-shaped fishing weights and a cork fishing float were used.
Time measurement was a major issue in many of Galileo’s experiments. For his pendulum experiments, Galileo seems to have compared the pendulums in pairs over the same time. For example, a person would be assigned to each pendulum of the pair and between the words “start” and “stop” each person would count the number of oscillations. This method was used for comparison in these experiments.
Pendulums nearly return to their release heights.
Galileo observed that the bobs of pendulums nearly return to their release height. Today this fact demonstrates conservation of energy, a principle not yet discovered in Galileo’s time. As a recreation, pendulums were released from different heights. The height the pendulum returned to was noted and compared to the release height. No quantitative measurements were made, but in every trial, the pendulum’s return height was very close to its release height. The estimated difference between the heights was no more that 3 mm for the range of string lengths used.
All pendulums eventually come to rest with the lighter ones coming to rest faster.
Galileo noted that lighter pendulums come to rest faster. As a test of this observation, two pendulums, nearly identical except for their bobs of different weights, were released at the same time and height. A bob of lead was hung with a string length of 28.9 cm. A bob of cork was hung to hang at 29.0 cm. The two were released at the same time after being pulled back about 5 degrees. After waiting for several minutes, the cork bob came to rest while the lead bob was still moving. More trials revealed the same result in agreement with Galileo.
The period is independent of the bob weight.
Cork and lead pendulums of the same length Galileo claimed to
have hung pendulums of cork and lead from his ceiling and measured their periods to be the same. As a test, a pendulum 29.0 cm long of cork and a pendulum 28.9 cm long of lead were used. Both were suspended and released simultaneously from the same height. For five trials, the cork was allowed to travel through ten oscillations and compared to the number of oscillations of the lead during that time. Then the process was reversed for five additional trials. The lead pendulum was allowed to travel through ten oscillations and the oscillations of the cork were counted. The results are below.
| Number of cork oscillations | 10.0 | 10.0 | 10.0 | 10.0 | 10.0 | 9.9 | 10.0 | 10.0 | 9.9 | 10.0 |
|---|---|---|---|---|---|---|---|---|---|---|
| Number of lead oscillations | 10.0 | 10.0 | 9.9 | 10.1 | 10.1 | 10.0 | 10.0 | 10.0 | 10.0 | 10.0 |
The average number of oscillations for the cork bob was 9.98. The average number of oscillations for the lead bob was 10.01. The percent difference between these averages is 0.300%. For any one measurement, the highest discrepancy was 0.1 oscillation or 1%. Galileo’s discovery holds up very well in this test.
The period is independent of the amplitude.
Galileo claimed that the pendulum period was independent of the amplitude in Two New Sciences. Scholars debate whether he meant that the periods are exactly the same of that they differ very little. As a test of whether they are exactly the same, two pendulums with identical lead bobs were suspended 28.9 cm. They were released at the same time from different angles. One was pulled back about 5 degrees while the other was released from about 45 degrees. The pendulum pulled back five degrees was allowed to travel through thirty cycles, and the numbers of oscillations of the other pendulum during this time were counted. The data is below.
| Oscillations of 5 degree release | 30.0 | 30.0 | 30.0 | 30.0 | 30.0 |
|---|---|---|---|---|---|
| Oscillations of 45 degree release | 29.5 | 29.6 | 29.5 | 29.5 | 29.0 |
The pendulum which traveled through the larger angle had a longer period. It averaged 29.42 oscillations during 30 swings of the other, and had fewer oscillations in every trial. Clearly, pendulums with different amplitudes do not have the same period. In fact, it appears that pendulums with larger amplitudes have longer periods. The difference is quite small, though. Whether Galileo’s claim is true depends on interpretation of the claim, but the interpretation that identical pendulums of different amplitudes have periods independent of amplitude is false.
The square of the period varies directly with the length.
Lead pendulums with one string about four times as long as the
other Galileo found that the period squared is proportional to the length for a pendulum. As a test, lead pendulums differing in length by factors of two and four were compared. Pendulums of lengths 24.0 cm and 50.5 cm were released simultaneously. The shorter pendulum was allowed to pass through 28 cycles as the oscillations of the longer one were counted. The data is below.
| 24.0 cm string | 28.0 | 28.0 | 28.0 | 28.0 | 28.0 |
|---|---|---|---|---|---|
| 50.5 cm string | 20.0 | 19.9 | 19.8 | 20.0 | 19.9 |
Then pendulums of lengths 24.0 cm and 99.4 cm were compared. They were released simultaneously. The shorter pendulum was allowed to pass through 20 cycles as the oscillations of the longer pendulum were counted. The data for these trials is below.
| 24.0 cm string | 20.0 | 20.0 | 20.0 | 20.0 | 20.0 |
|---|---|---|---|---|---|
| 99.4 cm string | 9.75 | 9.25 | 9.7 | 10.0 | 9.75 |
For the first data set, the longer pendulum averaged 19.9 cycles during the shorter ones 28. 19.9/28 is 0.711. The square root of the ratio of their lengths is 0.689. The percent different between these ratios is 3.14%. For the second data set, the longer pendulum averaged 9.69 cycles during the shorter pendulum’s 20. The ratio between these two numbers is 0.485. The square root of the ratio of their lengths is 0.491. The percent difference between these ratios is 1.23%. For both experiments, the relationship discovered by Galileo holds well.
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Question/ Purpose:
What do you want to find out? Write a statement that describes what you want to do. Use your observations and questions to write the statement.
The purpose of this project is to find out how can the period of a pendulum be increased.
Identify Variables:
When you think you know what variables may be involved, think about ways to change one at a time. If you change more than one at a time, you will not know what variable is causing your observation. Sometimes variables are linked and work together to cause something. At first, try to choose variables that you think act independently of each other.
Variables that may affect the period of a pendulum and we will test in this project are:
- Length of Pendulum
- Bob weight
- Release height or release angle
This is how you define variables while studying on the effect of pendulum length on the period.
Independent variable (also known as manipulated variable) is the length of pendulum.
Dependent variable (also known as responding variable) is the period of pendulum.
Constants are the bob weight and the release angle.
You can use this format and define the variables where bob weight or release angle are the independent variables.
Hypothesis:
Some possible Hypothesis are:
1. Period of Pendulum will increase with the length of pendulum.
2. Period of pendulum will decrease by increasing the bob weight.
You may select one of these hypothesis or make up a new one.
Experiment Design:
Design an experiment to test each hypothesis. Make a step-by-step list of what you will do to answer each question. This list is called an experimental procedure. For an experiment to give answers you can trust, it must have a “control.” A control is an additional experimental trial or run. It is a separate experiment, done exactly like the others. The only difference is that no experimental variables are changed. A control is a neutral “reference point” for comparison that allows you to see what changing a variable does by comparing it to not changing anything. Dependable controls are sometimes very hard to develop. They can be the hardest part of a project. Without a control you cannot be sure that changing the variable causes your observations. A series of experiments that includes a control is called a “controlled experiment.”
Experiment 1: (Make a pendulum for initial observations)
Introduction:
A pendulum can be constructed using a long string and a weight. A lead fishing weight is a great mass. A meter long string of almost any non elastic material can be used for this homemade pendulum.
Procedure:
- Tie the weight onto the end of the string.
- Measuring from the center of the weight mark off 10 cm lengths along the string.
- Hold the string at the one meter mark and start it swinging. What do you see? What’s Going On?
Observations:
When you pull the pendulum to the side gravity pulls it back toward the center.
You can feel this force as you pull the pendulum to the side.
The pendulum moves fastest at the bottom of its swing and slower at the ends, in fact it stops and reverses its direction at the ends of its swings. At the bottom of its swing there is no force on the pendulum causing it to continue or to stop its swing, the inertia of its motion carries it through the bottom and up the other side.
Longer pendulums take longer to complete one cycle of swing.
The energy of motion, kinetic energy is maximum at the bottom of the swing and zero at the ends of the swing. The potential energy from gravity is greatest at the ends of the swing and least at the bottom. The energy in a pendulum goes back and forth between kinetic and potential.
Experiment 2: (Test the effect of bobs weight in the period of a pendulum)
Introduction: Period of a pendulum is the amount of time that it takes for a pendulum to do one complete swing and come back to it’s start point. Accurate measurement of one swing is not easy, so we count the number of swings per minute, then we divide 60 by that number. For example if the pendulum swings 30 times per minute, its period will be calculated by dividing 60 by 30 and the result will be 2. So the period of a pendulum that swings 30 times per minute is 2. In the same way If the pendulum swings 85 times per minute, then its period is 0.70, so the period is not always an integer number.
Procedure:
To test the effect of bobs weight in the period of a pendulum we make a pendulum and test it’s period. then we double the weight of the bob and repeat the test again. One simple way of doing that is use a bolt as a bob. Then use two bolts together as a bob. Record the results in a table like this.
| bob’s weight | Pendulum Period |
| 5 grams (1 bolt) | |
| 10 grams | |
| 15 grams | |
| 20 grams |
Need a control Experiment? Use another identical pendulum as your control; however, in the control pendulum do not change the bob’s weight. By examining and observing the period of this pendulum, you can show that the period change in your experimental pendulum was caused by changes in the bob’s weight, and not an unknown natural phenomena.
Experiment 3: (Test the effect of pendulum length)
Procedure:
To test the effect of length in the period of a pendulum we make a pendulum and test it’s period. Then we double the length of pendulum and repeat the test again. One simple way of doing that is to use a one feet string for first test and a 2 feet string for the second test. Record the results in a table like this.
| Pendulum Length | Pendulum Period |
| 5 inches | |
| 10 inches | |
| 15 inches | |
| 20 inches |
Need a control Experiment? Use another identical pendulum as your control; however, in the control pendulum do not change the length. By examining and observing the period of this pendulum, you can show that the period change in your experimental pendulum was caused by changes in the length, and not an unknown natural phenomena.
Experiment 4: (Test the effect of release height)
Procedure:
To test the effect of release height in the period of a pendulum we make a pendulum and test it’s period with a certain release height. Then we repeat the test with a different release height. Record the results in a table like this.
| Release Height | Pendulum Period |
| 5 inches | |
| 10 inches | |
| 15 inches | |
| 20 inches |
Need a control Experiment? Use another identical pendulum as your control; however, in the control pendulum do not change the release height. By examining and observing the period of this pendulum, you can show that any period change in your experimental pendulum was caused by changes in the release height, and not an unknown natural phenomena.
Materials and Equipment:
This is a list of material that you may use in constructing a pendulum and performing your experiments.
- string, over a meter, strong enough it will not stretch when loaded with the weight
- a weight, lead fishing weight, steel nut, film can full of sand or clay etc.
- a meter stick
- a marker pen
- a stopwatch
- graph paper
Results of Experiment (Observation):
Experiments are often done in series. A series of experiments can be done by changing one variable a different amount each time. A series of experiments is made up of separate experimental “runs.” During each run you make a measurement of how much the variable affected the system under study. For each run, a different amount of change in the variable is used. This produces a different amount of response in the system. You measure this response, or record data, in a table for this purpose. This is considered “raw data” since it has not been processed or interpreted yet. When raw data gets processed mathematically, for example, it becomes results.
Calculations:
While measuring the pendulum period, you may see how many times does the pendulum swing in 10 seconds. Then divide 10 by that number to measure period in seconds.
Summary of Results:
Summarize what happened. This can be in the form of a table of processed numerical data, or graphs. It could also be a written statement of what occurred during experiments.
It is from calculations using recorded data that tables and graphs are made. Studying tables and graphs, we can see trends that tell us how different variables cause our observations. Based on these trends, we can draw conclusions about the system under study. These conclusions help us confirm or deny our original hypothesis. Often, mathematical equations can be made from graphs. These equations allow us to predict how a change will affect the system without the need to do additional experiments. Advanced levels of experimental science rely heavily on graphical and mathematical analysis of data. At this level, science becomes even more interesting and powerful.
Conclusion:
Using the trends in your experimental data and your experimental observations, try to answer your original questions. Is your hypothesis correct? Now is the time to pull together what happened, and assess the experiments you did.
Collected information and the results of our experiments indicate that the following formula can be used to calculate the period of a pendulum with a certain length.
Where g = 9.78 M/S/S and L is the length of pendulum.
At a given place on the earth, where g is constant, the formula shows that the oscillation period T depends only on the length, l, of the pendulum. Moreover, the period remains constant even when the amplitude of the vibration diminishes due to the losses in the system such as the resistance of the air and friction of the potentiometer.
Related Questions & Answers:
What you have learned may allow you to answer other questions. Many questions are related. Several new questions may have occurred to you while doing experiments. You may now be able to understand or verify things that you discovered when gathering information for the project. Questions lead to more questions, which lead to additional hypothesis that need to be tested.
Possible Errors:
If you did not observe anything different than what happened with your control, the variable you changed may not affect the system you are investigating. If you did not observe a consistent, reproducible trend in your series of experimental runs there may be experimental errors affecting your results. The first thing to check is how you are making your measurements. Is the measurement method questionable or unreliable? Maybe you are reading a scale incorrectly, or maybe the measuring instrument is working erratically.
If you determine that experimental errors are influencing your results, carefully rethink the design of your experiments. Review each step of the procedure to find sources of potential errors. If possible, have a scientist review the procedure with you. Sometimes the designer of an experiment can miss the obvious.
References:
Visit a local library and find a physics book that has discussions about pendulum.
1. How does Earth rotation affect the pendulum movement?
2. Is the pendulum movement affected by being in other part of the world?
The Foucault pendulum was first demonstrated in 1851 by yet another French scientist; his name was Jean Foucault. The Foucault pendulum is nothing more than a very long pendulum suspended from a well-oiled ball-and-socket joint overhead, so it is free to swing in any direction.
Foucault set up such a pendulum in the Pantheon in Paris, and set it swinging north to south. As hours passed, however, the direction in which the pendulum was swinging moved around in a clockwise direction. After a while, the pendulum was swinging northeast-southwest; after a while longer, it was swinging east-west, then southeast-northwest, then north-south again. What causes this change in the pendulum’s direction of swing? The rotation of the Earth, of course.
It is easiest to visualize what’s happening to a Foucault pendulum by imagining the simplest case: a Foucault pendulum set up at the North Pole of the Earth. We set the pendulum swinging in a particular direction: toward and away from the star Betelgeuse, to take a concrete example.
What an observer on Betelgeuse sees:
- The direction of the pendulum’s swing is constant.
- The Earth rotates counterclockwise (looking down at the North Pole), completing one rotation in 24 hours.
What an observer on Earth sees:
- The Earth is stationary relative to the observer.
- The direction of the pendulum’s swing rotates clockwise (looking down at the North Pole), completing one rotation in 24 hours.
Whether one says the Earth is rotating or the pendulum is rotating depends on one’s point of view. The important fact (independent of where you’re standing) is that the Earth and the pendulum’s swing are rotating relative to each other. If the Earth did not rotate on its axis, the direction of swing of a Foucault pendulum would remain fixed relative to the surface of the Earth.
More information about Foucault pendulums (pendula?) is available from the California Academy of Sciences.
