- An object swinging at the end of a string forms a pendulum. In this investigation you will let a lead ball swing from different lengths of string. For each length, you will count the number of swings the pendulum makes in one minute. This value represents the frequency of the pendulum's motion. You will then graph your data and use the graph to predict frequency values for pendulum lengths you did not actually measure.
MATERIALS:
String, 1 m long
*Lead ball with hole or hook
meter stick
Masking tape
Graph paper
Clock or watch that indicates seconds*You can use a large fishing sinker or large metal nut. Because you measure the length of a pendulum from the center of mass of the weight, to the pivot point at the top of the string, a sphere is an easier shape to work with.
PROCEDURE:
- Before you begin, write a hypothesis that describes how YOU think the length of a pendulum affects its frequency.
1. Attach one end of a 1-meter-long string to a lead ball. Find the point on the string that is 80 cm from the center of the ball (center of mass). Place the bottom edge of a piece of masking tape across the string at that point. Use the masking tape to suspend the pendulum from the side of a table or other support.
2. Hold the pendulum ball about 10 cm to the side and release it. Make sure the ball swings freely. Count the number of complete swings in one minute. A complete swing is from the point of release to the other side and back to the same point. Record your observation in the table provided. Record the total number of complete swings your pendulum had for one minute, in DATA TABLE 1.
3. Change the length of the pendulum to 70 cm. Again count the number of complete swings in one minute. Record your observation in DATA TABLE 1.
4. Repeat the measurement of the number of complete swings with the pendulum length at 60 cm, 50 cm, 40 cm, and 30 cm. Again record your observations in DATA TABLE 1.
DATA TABLE 1: Number of complete swings observed per minute for different lengths of a pendulum Pendulum Length
(in cm)Number of
Complete Swings
(in one minute)80 
70 60 50 40 30 CALCULATIONS:
- There are many ways to deal with raw data, and put it into a form that we can both understand it in terms of our hypothesis, and predict from it. A graph is a wonderful tool for interpreting data, and in this investigation, the best method of dealing with our data.
5. Make a graph of your data. Remember there are some basic "rules" for graph construction. Every graph needs a title and both axis of the graph need numerical values and labels telling what they represent, and in what units of measurement the numbers are in. We also do things "by convention". This means we usually do it a certain way, to be consistent with other graphs. By convention, we graph a variable (the thing we observe) and a constant (that which we have set). We put the variable on the vertical axis, and the constant on the horizontal axis. Our variable here is the number of complete swings in one minute, and the constant is the length of the pendulum.
- After you plot the points from the pairs of data in your DATA TABLE, the next step is to fit a line to the data points. When we take data in an investigation, it often contains some error from our observations. This is normal. We could have miscounted, or our timing was not exact. We fix this in the graph, by fitting the line to average our data. First, look at the data points and decide if it is a straight line, or a curved line. Now we draw a line through our data points that best fits all the points. If it is a straight line we always use a ruler or straight edge to draw the line, and if its is a curved line we have to draw it free-hand. We have to be careful to draw a smooth curve. All of our data points will not necessarily be on the line, but the line best "averages" our points.
- Now you know how to properly fit a line to experimental data for future investigations.
PREDICTING FROM YOUR GRAPH:
6. Describe the line that passes through the points plotted on your graph.
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7. Now use your graph to predict the behavior of a pendulum in conditions you did not measure, but are represented on your graph.
How many swings per minute would you predict for a pendulum 55 cm long?
_________ swings / minute
How long a pendulum would you predict will make 60 swings in one minute (this is one per second)?
_________ cm
CONCLUSION:
How does the number of swings change as the pendulum is shortened?
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FURTHER INVESTIGATION:
- The length of time for a complete swing of a pendulum is called the period of a pendulum. The period can be calculated in seconds by dividing the number of swings in one minute, by 60.
- (Number of swings/minute)(1 minute/60 seconds)
Determine the period of the pendulum for each of the lengths measured (round the answers to the nearest whole number). Put the answers in DATA TABLE 2.
DATA TABLE 2: Periods calculated from observations of different lengths of a pendulum. Pendulum Length
(in cm)Period
of Pendulum
(per second)80 70 60 50 40 30 - Make a graph that shows how the period of the pendulum changes as the length changes. Don't forget what you learned about graphing when you did the first graph. Do the points on your graph lie on a straight line?
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- There are other investigations you could do with a pendulum. Write a hypothesis about the effect of how far back from center you start the pendulum swinging, on the number of complete swings the pendulum will make. Now design an investigation for your hypothesis. There may be other aspects of a pendulum that you can think of to investigate. Think about it.
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- Before you begin, write a hypothesis that describes how YOU think the length of a pendulum affects its frequency.
GRAPHING PENDULUM MEASUREMENTS