course Phy 231
introductory pendulum experimentPhy 231
Your 'introductory pendulum experiment' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Introductory Pendulum Experiment
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As on the first object-down-a-ramp experiment, this experiment doesn't require a major time committment. If you mess something up you get feedback and will be able to fix it. However, as before, do your best to get it right the first time.
In this experiment you will make a simple pendulum and observe how its frequency of oscillation varies with its length.
To make a pendulum tie a light string or thread around a relatively small dense object. In the absence of anything more convenient you could use a couple of CDs or DVDs with a string or thread tied through the middle. A smaller and denser object would be preferable, but not so much that you should take a lot of time trying to locate one. The string or thread should be about 4 feet long.
Hold the string so that the length from the point at which you are holding it to the center of the object is about equal to the distance from your wrist to your fingertips.
• Measure the length of this pendulum, from the point where you hold it to the center of the suspended mass, as accurately as you can.
• Start the pendulum oscillating, but don't make it swing too far--keep the distance from one end of the swing to the other less than half the length of the pendulum.
• Using a clock with a second hand, determine how many times this pendulum oscillates in 60 seconds. Repeat your count at least a few times, and continue until you are sure you know to the nearest whole cycle how many times it oscillates back and forth in a minute.
Repeat with a pendulum whose length is equal to the distance from your fingertip to your elbow.
Repeat once more with a pendulum whose length is equal to the distance from your toes to your hip.
In the box below
• Describe how you constructed your pendulum and out of what (what you used for the mass, its approximate dimensions, what it is made of, what sort of string or thread you used--be as specific as possible).
• Describe its motion, including an estimate (you don't have to measure this, just give a ballpark estimate) of how far it swung from side to side and how this distance varied over the time you counted.
• Give the lengths and the numbers of cycles counted, preferably in the form of a simple table so a reader can scan the data easily. Be sure you specify the units in which you measure the lengths (e.g., nanometers, millimeters, centimeters, inches, feet, miles).
• Describe what you mean by a 'cycle'. Different people might mean different things, but there are only a couple of reasonable meanings so as long as you describe what you mean we will all understand what you measured.
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For the first pendulum experiment, I used a 4ft pendulum made of a very skinny and light rope, with one of the large washers provided in the lab kit. The washer had a diameter of 77mm. In 60sec the rope made 26 cycles. I define a cycle by each time the pendulum goes to the left and right. The rope oscillated approximately two feet on either side of the center (or my hand).
I used the same rope and washer for the second run but this time only used 19in of the rope. In 60sec, the rope completed 40 cycles. The rope oscillated approximately 9in from the center.
I used the same rope and washer for the third run. I used 37in of rope this time. In 60sec the pendulum completed 31 cycles. The rope oscillated approximately 18in from center.
48in of rope: 26 cycles
19in of rope: 40 cycles
37in of rope: 31 cycles
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On a piece of paper sketch a graph of the number of cycles vs. the length of the pendulum.
• The lengths will go along the horizontal axis, the one usually labeled as the 'x axis'.
• The numbers of cycles will be represented on the vertical axis, the one usually labeled as the 'y axis'.
• Any time you graph quantity A vs. quantity B, you follow the 'y vs. x' convention with quantity A on the y or vertical axis, quantity B on the x or horizontal axis.
• Decide on a scale to use for each axis are mark off a consistent scale for each. The scale of one axis is independent of the scale of the other.
• Use a scale and graph size that will allow you to tell easily whether the three points on your graph lie on or close to a straight line, or whether the three points seem to lie on a nonlinear curve (i.e., a curve which is clearly not a straight line).
Imagine that you obtained an extensive data set, with hundreds of different lengths. Based on what you observed for your three lengths, and on your graph:
• What do you think the graph would look like?
• Would it be a straight line or a curve?
• Would it be increasing or decreasing? ... at an increasing or decreasing rate?
• What would happen to frequency as length became very small? What if length became very large?
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Based on my three data points, if I saw a graph of hundreds of data points the graph would clearly show a decreasing line. My graph wasn’t a straight line but it was close to one. I believe that if one had more data then the graph would be a straight line. The rate at which it is decreasing would then be constant. As length becomes larger, frequency decreases. And as length decreases, frequency increases.
If the line remains straight, then it will intersect the horizontal axis. At this point, what will be the frequency of the pendulum, and how would you then describe its mode? Is this reasonable?
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&&&&.&# If the line intersects the horizontal axis, then the number of cycles would be equal to zero. This would never happen. The graph would be asymptotical to the x-axis. There would always be cycles in this experiment even if it was less than one cycle.
Your instructor is trying to gauge the typical time spent by students on these experiments. Please answer the following question as accurately as you can, understanding that your answer will be used only for the stated purpose and has no bearing on your grades:
• Approximately how long did it take you to complete this experiment?
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It took approximately 30 minutes to complete this assignment.
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You may add optional comments and/or questions in the box below.
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Good data.
Good answer to the questtion.