#$&*
course Phys201
6/17@9:46pm. As I stated in earlier note, I redid this entire experiment because initially I did not preform correctly. I attached the new lab to the bottom of the old one so you could see both.
introductory pendulum experiment#$&*
Phys201
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.
** Introductory Pendulum Experiment_labelMessages **
I will be emailing you the graphs I sketched.
** **
Your answer (start in the next line):
9,152,.39
13.5,143,.42
8,134,.45
27,120,.5
36,104,.58
54,92,.65
72,80,.75
108,68.88
144,60,1
your brief discussion/description/explanation:
I included all of my times in order to be more precise. As length in cm increases, the number of cycles decreases. The time for one cycle also increases with length.
************`
#$&*
1. According to your graphs, complete the following tables
length in cm
number of cycles
time for one cycle
1
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
length in cm number of cycles time for one cycle
9 152 .39
13.5 143 .42
18 134 .45
27 120 .5
36 104 .58
54 92 .65
72 80 .75
108 68 .88
144 60 1
#$&* length, count, period for given lengths
length in cm
number of cycles
time for one cycle
10
30
50
70
90
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
ength in cm number of cycles time for one cycle
9 152 .39
13.5 143 .42
18 134 .45
27 120 .5
36 104 .58
54 92 .65
72 80 .75
108 68 .88
144 60 1
This is a repeat of your previous table. This is not what was requested.
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@&
`` You were previously asked to make graphs of your data, one graph of number of cycles vs. length, the other of time required for a single cycle vs. length. The present question asks you to complete a table based on your graphs.In this table the values of the length of the pendulum were specified. You need to go to your graph of time for one cycle vs. length, determine the number of cycles that would, according to your graph, correspond with each of these lengths. These times will not be the same as the times on your original table, since the lengths will be different. These times will constitute the second column of your table.You will also go to your graph of number of cycles observed vs. length and determine the number of cycles your graph predicts for each of the lengths given here. These values will constitute the third column of your table.
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#$&* length, count, period for given counts
length in cm
number of cycles
time for one cycle
0.5
0.9
1.3
1.7
2.1
2.5
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
ength in cm number of cycles time for one cycle
9 152 .39
13.5 143 .42
18 134 .45
27 120 .5
36 104 .58
54 92 .65
72 80 .75
108 68 .88
144 60 1
@&
`` You were previously asked to make graphs of your data, one graph of number of cycles vs. length, the other of time required for a single cycle vs. length. The present question asks you to complete a table based on your graphs.In this table the values of the number of cycles of the pendulum were specified. You need to go to your graph of number of cycles observed vs. length, determine the length that would, according to your graph, correspond with each of these numbers of cycles. These lengths will not be the same as the times on your original table, since the numbers of cycles will be different. These lengths will constitute the first column of your table.You will also go to your graph of time per cycle vs. length and determine the \time required for a cycle for the length you determined. These values will constitute the third column of your table.
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#$&* length, count, period for given periods
2. Is the graph of # of cycles vs. length in cm constant, increasing or decreasing? Is it doing so at an increasing, constant or decreasing rate?
On this and on all questions, insert your answer after the 'Answer:' prompt, and include a brief explanation of how you arrived at your answer.
Your answer (start in the next line):
It is decreasing at a increasing rate.
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`` A decreasing graph that remains positive cannot decrease at an increasing rate.
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#$&* graph of count vs length
3. Is the graph of time required for one cycle vs. length in cm constant, increasing or decreasing? Is it doing so at an increasing, constant or decreasing rate?
Your answer (start in the next line):
It is increasing at an increasing rate.
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`` If your axes are reversed, with time required for a cycle on the horizontal rather than the vertical axis, this graph will increase at a increasing rate. However if the axes are in the order dictated by the description (time per cycle vs. length) the length will be the independent variable and will be on the horizontal axis. In this case the graph will increase at a decreasing rate.
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#$&* graph of period vs length
4. How much difference is there between your first two lengths, and how much difference between the number of cycles counted in 60 seconds?
Your answer (start in the next line):
There is a 4.5 cm difference in my first two lengths. There is 9 cycles difference.
#$&* diff between lengths, between counts
5. How much difference is there between your first two lengths, and how much difference between the corresponding times required to complete a cycle?
Your answer (start in the next line):
There is a 4.5 cm difference between the first two lengths. There is a .03 difference in time.
#$&* diff between lengths, periods
6. How much difference is there between your last two lengths, and how much difference between the number of cycles counted in 60 seconds?
Your answer (start in the next line):
#$&* diff between last two lengths, counts
7. How much difference is there between your last two lengths, and how much difference between the corresponding times required to complete a cycle?
Your answer (start in the next line):
There is a 36 cm difference between the last two lengths. There is a .12 time difference.
#$&* diff between last two lengths, periods
8. Is your graph of number of cycles counted vs. length in cm steeper, on the average, between the first two lengths or between the last two lengths?
Your answer (start in the next line):
Steeper between the last 2 lengths.
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The only way this would occur is if you reversed the order of your quantites, and graphd length vs. number of cycles.
The independent variable goes on the horizontal axis.
y vs. x has y on the vertical, x on the horizontal axis.
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#$&* count vs. length steeper between 1st two or last two pts
9. Is your graph of time required to complete a cycle vs. length in cm steeper, on the average, between the first two lengths or between the last two lengths?
Your answer (start in the next line):
Steeper between first 2 lengths.
#$&* period vs. length steeper between 1st two or last two pts
10. The curve you sketched for your graph of (time required to complete a cycle) vs. (length) cannot possibly pass through the center of each of your points.
What is the greatest vertical distance between a point of your graph and the curve?
What do you think is the least vertical distance?
You will answer these questions at the 'your answer' prompt a little ways below.
(For example, in the figure below a curve has been constructed based on three data points. The first and third data point lie slightly above the curve, the second point slightly below. The second point is probably the one which lies furthest from the curve, at a distance of approximately .03 vertical units below. This distance is roughly estimated based on the scale of the graph. The first point is perhaps .01 vertical units above the curve, and the third is perhaps .02 units above.)
Your answer (start in the next line):
The greatest vertical distance would be at the 54 cm point. The least vertical distance would be at the first point at 9 cm.
#$&* greatest, least vert dist between datapt and curve
After the 'Your Answer' prompt below, insert your answers to the following :
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.
Describe what you mean by a 'cycle'. Different people might mean different things, but there are only a couple of reasonable meanings. As long as you describe what you mean we will all understand what you measured.
'Frequency' means the number of cycles in a unit of time. Your counts are frequencies, in cycles/minute. 'Period' means time required for a cycle. Explain how you used your observed frequencies to obtain the periods of the nine pendulums in this experiment.
Your answer (start in the next line):
I constructed my pendulum out of 2 regular sized DVDs and sewing thread. I attached the thread by looping it through the holes on the DVDs.
The motion was for the most part left to right but there were some issues with rotation of the DVDs. When using the 9cm of thread the distance it swung was about 4 inches wide. As the thread distance got larger it swung wider. At its longest length at 144 cm it swung about 12 inches wide.
A cycle is when it moves from left to right. So I counted when it went to the right then doubled my answer.
So for frequency I counted the number of times the DVDs went to the right. I then doubled that number to get the number of cycles. To obtain period I divided 60 (60 sec in a min) by the number of cycles.
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You did not use your graphs to complete the specified tables in the first half of the experiment.
It also seems you might have reversed the axes of your graphs.
&#Please see my notes and submit a copy of this document with revisions, comments and/or questions, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
Be sure to include the entire document, including my notes.
&#
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&&&&&&&&&&&&&&&&&&&Pendulum Experiment
Copy this document into a text editor (e.g., Notepad; preferably NOT into a word processor or html editor, e.g., NOT into Word or FrontPage).
• Follow the instructions, fill in your data and the results of your analysis in the given format.
• Regularly save your document to your computer as you work.
• When you have completed your work:
Highlight the contents of the text editor, and copy and paste those contents into the indicated box at the end of this form.
Click the Submit button and save your form confirmation.
In this experiment you will make a simple pendulum and observe how its frequency of oscillation varies with its length.
The goals of this experiment include the following:
• Practice sketching graphs.
• Practice interpreting graphs.
• Obtain a concrete example which will be useful in understanding the essential concept of rate of change.
• Enhance your ability to make accurate observations.
• Quantify limits on the accuracy of data and the effect of these limits.
• Obtain information necessary to use a pendulum as an accurate timing device.
To make the pendulum:
• Tie a light string or thread, about as long as you are tall, 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 ring might also be a good choice (but avoid using a ring with a lot of value).
A smaller and denser object would be preferable, but don't take a lot of time trying to locate the smallest densest object you can find. Just about anything will do if it is smaller than an average fist and dense enough to sink if it is placed in water (you won't actually be placing the object in water).
• The string or thread should be about 4 feet long.
If you have a ruler or a measuring tape marked in centimeters, you may use it. If you don't, open and print out the file at the link ruler, which can be used to obtain sufficiently accurate measurements.
You will count and time oscillations of a series of simple pendulum, of 9 different lengths.
Determine the lengths of the pendulums to be used in your experiment:
Take your height in inches, subtract 30 and divide your result by 5. Round your result off to the next whole number. This will be the length in centimeters of your first pendulum. (For example if you are 91 inches tall (unlikely but not impossible), you would subtract 30 to get 61, then divide 61 by 5 to get 12.2. This rounds off to 12, so your pendulum would be 12 cm long).
Double the length of your first pendulum. This is the length of your third pendulum.
Double the length of your third pendulum. This is the length of your fifth pendulum.
Double the length of your fifth pendulum. This is the length of your seventh pendulum.
Double the length of your seventh pendulum. This is the length of your ninth pendulum.
Write down the numbers 1 through 9 in the first column of a table, and the lengths you have obtained in the second column, each length opposite the appropriate number. For example if your first pendulum was 12 cm long your table would look something like the following:
number length
1 12
2
3 24
4
5 48
6
7 96
8
9 192
Note that you aren't asked here to enter your table.
Sketch a rough graph of your lengths
You are going to make a graph of this information.
Sketch the graph by hand (perhaps using the template below). Don't use the computer to construct your graphs in this experiment.
If you want to print and use the template below you may do so, or you may make a rough sketch something like the figure below. Don't bother to use a ruler and make a meticulous graph. Any reasonable freehand sketch is fine (or again, if you wish, you can print the figure below and use it).
Now make a graph of pendulum length vs. number, based on your table. This graph will have length on the vertical axis and the pendulum number on the horizontal. The graph will look something like the one below, which however is based on the unlikely 12 cm initial length for the 91-inch-tall student.
Sketch a smooth curve through the points on your graph. This will give you a graph much like the one below:
Estimate the pendulum lengths which would correspond to numbers 2, 4, 6, and 8.
Complete the table by filling in the lengths corresponding to pendulums number 2, 4, 6 and 8, as estimated from your graph. Try to make reasonable estimates, but don't take a lot of time to make your estimates exact. If you are 91 inches tall your table might be as indicated below:
number length
1 12
2 15
3 24
4 35
5 48
6 70
7 96
8 140
9 192
Time and count oscillations for the nine different pendulums
Hold the string so that the length from the point at which you are holding it to the center of the object is equal to the first distance on your table (e.g., for the table given above that distance would be 12 cm).
• 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. To keep it swinging you might need to use the fingers in which you are holding it to slightly nudge the pendulum.
• Using a clock with a second hand, determine how many times this pendulum oscillates in 60 seconds. A complete oscillation, or a complete cycle, is from one extreme point to the other and back. If you count every time your pendulum changes direction, you are counting half-cycles (it's fine to count half-cycles; if you do just be sure to divide by 2 to get the number of complete oscillations). Repeat your count at least a few times, and continue until you are sure you know to the nearest whole cycle (or if you prefer to the nearest half-cycle) how many times it oscillates back and forth in a minute. It shouldn't take more than a few trials to get in the habit of counting accurately, but if you don't count carefully it might. A surprising number of students have difficulty making an accurate 60-second count, and some need the practice.
Repeat this for each of the nine lengths on your table.
Construct a table of the number of oscillations observed vs. the length of the pendulum. For the example given here, corresponding to a person 91 inches tall, the table might look something like the following (the numbers in this example shouldn't be regarded as particularly accurate or useful; your counts should be more accurate than these):
length number of cycles
12 85
15 75
24 60
35 50
48 40
70 35
96 30
140 25
192 20
Graph your data
You will graph the data in your table.
You may if you wish use the template below to help you construct your graph; you may if you wish print out the figure, or simply make a hand sketch--again be reasonably accurate but don't take the time to be be overly meticulous.
A graph of the sample data for the very tall student would look like the following:
Figure out the time required per oscillation at each length
You know how many times each pendulum oscillated in 60 seconds. From this information you can figure out for each length how many seconds, and/or what fraction of a second, was required for a single oscillation. You should be able to figure out how to do this. Make a table showing the number of seconds required per oscillation vs. the length of the pendulum in cm. The figure below corresponds to the example of the 91-inch-tall individual, and these results are not to be regarded as particularly accurate.
length time for one cycle
12 0.7
15 0.8
24 1
35 1.2
48 1.5
70 1.7
96 2
140 2.4
192 3
Construct a graph of the time required for a single oscillation vs. the length of the pendulum. You may use the graph below as a template:
For the present example the graph might look like this:
Sketch a smooth curve to represent the data. A good smooth curve for the sample data represented above might look like this:
The curve should come as close as possible, on the average, to the data points, but it should not 'wobble around' in an attempt to actually go through any of the data points. The figure below represents a smooth curve that does wobble around a lot, and this isn't what you want here:
After the 'Your answer' prompt about half a page below you will report your data, using the precise format described below. All reported data will be collected and reported back to the rest of the class (your data will be reported anonymously--only I will know whose data is which), and if anyone's data is not in the prescribed format, it might be necessary to ask everyone to report their data again.
Be sure to save your information as you type it into the copied document. Keep your copies; if the data is required later you will then be easily able to access it.
After the prompt on the first line below the 'Your Answer' prompt, report your vccs email address, the length of the shortest pendulum in centimeters, the number of cycles counted for this pendulum in 60 seconds, and the time required for one complete cycle. Put a comma between each pair of entries. So for the example of the 91-inch-tall student, the first line would read
abc123@email.vccs.edu, 12, 85, .7
Each subsequent line will appear in the same format. So the next two lines for this example student would be
abc123@email.vccs.edu, 15, 75, .8
abc123@email.vccs.edu, 24, 60, 1
It should take you only a couple of minutes to enter this information. You should as usual use copy-and-paste to insert your email address (this will save you time and will ensure that you have given the correct address).
Lines have been provided for up to 8 lengths; however if you followed the instructions you should have observed pendulums of only 6 or 7 different lengths. Extra lines can be left blank.
Your answer (start in the next line):
6,95,.63
9,86,.70
12,78,.77
15,71,.85
24,60,1
37,49,1.22
48,41,1.46
75,34,1.76
96,30,2
6 95 .63
9 86 .70
12 78 .77
15 71 .85
24 60 1
37 49 1.22
48 41 1.46
75 34 1.76
96 30 2
your brief discussion/description/explanation:
I included all of my times in order to be more precise. As length in cm increases, the number of cycles decreases. The time for one cycle also increases with length.
************`
#$&*
1. According to your graphs, complete the following tables
length in cm number of cycles time for one cycle
10 82 .75
30 52 1.2
50 39 1.49
70 36 1.7
90 30 1.9
110 27 2.2
130 23 2.6
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
10 82 .75
30 52 1.2
50 39 1.49
70 36 1.7
90 30 1.9
110 27 2.2
130 23 2.6
#$&* length, count, period for given lengths
length in cm number of cycles time for one cycle
200 10 2.5
120 30 2.21
32 50 1.21
14 70 .83
7 90 .65
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
200 10 2.5
120 30 2.21
32 50 1.21
14 70 .83
7 90 .65
#$&* length, count, period for given counts
length in cm number of cycles time for one cycle
.1 120 0.5
20 66.7 0.9
25 46.2 1.3
45 35.3 1.7
105 28.6 2.1
200 24 2.5
Enter the numbers from your table in the space below with one line for each length. Each line should contain the length, number of cycles and time for one cycle, separated by tabs.
Your answer (start in the next line):
.1 120 .5
20 66.7 .9
25 46.2 1.3
45 35.3 1.7
105 28.6 2.1
200 24 2.5
#$&* length, count, period for given periods
2. Is the graph of # of cycles vs. length in cm constant, increasing or decreasing? Is it doing so at an increasing, constant or decreasing rate?
On this and on all questions, insert your answer after the 'Answer:' prompt, and include a brief explanation of how you arrived at your answer.
Your answer (start in the next line):
The graph would be decreasing at a decreasing rate because with each point it gets less steeper.
#$&* graph of count vs length
3. Is the graph of time required for one cycle vs. length in cm constant, increasing or decreasing? Is it doing so at an increasing, constant or decreasing rate?
Your answer (start in the next line):
The graph would be increasing at a decreasing rate because with each point it gets less steeper.
#$&* graph of period vs length
4. How much difference is there between your first two lengths, and how much difference between the number of cycles counted in 60 seconds?
Your answer (start in the next line):
The difference between your first two lengths is 3cm. The difference between the number of cycles counted in 60 secs is 9.
#$&* diff between lengths, between counts
5. How much difference is there between your first two lengths, and how much difference between the corresponding times required to complete a cycle?
Your answer (start in the next line):
The difference between your first two lengths is 3cm. The difference between the corresponding times required to complete a cycle is .07 sec.
#$&* diff between lengths, periods
6. How much difference is there between your last two lengths, and how much difference between the number of cycles counted in 60 seconds?
Your answer (start in the next line):
The difference between the last two lengths is 21cm. The difference between the number of cycles counted in 60 secs is .24.
#$&* diff between last two lengths, counts
7. How much difference is there between your last two lengths, and how much difference between the corresponding times required to complete a cycle?
Your answer (start in the next line):
The difference between my last two lengths is 21. The difference between the corresponding times required to complete a cycle is 4sec.
#$&* diff between last two lengths, periods
8. Is your graph of number of cycles counted vs. length in cm steeper, on the average, between the first two lengths or between the last two lengths?
Your answer (start in the next line):
My graph of number of cycles counted vs, length in cm is steeper between the first two lengths.
#$&* count vs. length steeper between 1st two or last two pts
9. Is your graph of time required to complete a cycle vs. length in cm steeper, on the average, between the first two lengths or between the last two lengths?
Your answer (start in the next line):
My graph of time required to complete a cycle vs. length in cm is steeper between the first two lengths.
#$&* period vs. length steeper between 1st two or last two pts
10. The curve you sketched for your graph of (time required to complete a cycle) vs. (length) cannot possibly pass through the center of each of your points.
• What is the greatest vertical distance between a point of your graph and the curve?
• What do you think is the least vertical distance?
You will answer these questions at the 'your answer' prompt a little ways below.
(For example, in the figure below a curve has been constructed based on three data points. The first and third data point lie slightly above the curve, the second point slightly below. The second point is probably the one which lies furthest from the curve, at a distance of approximately .03 vertical units below. This distance is roughly estimated based on the scale of the graph. The first point is perhaps .01 vertical units above the curve, and the third is perhaps .02 units above.)
Your answer (start in the next line):
My eighth point was actually the most off. The least vertical distance would be between the first 2 points on the graph.
#$&* greatest, least vert dist between datapt and curve
After the 'Your Answer' prompt below, insert your answers to the following :
• 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.
• Describe what you mean by a 'cycle'. Different people might mean different things, but there are only a couple of reasonable meanings. As long as you describe what you mean we will all understand what you measured.
• 'Frequency' means the number of cycles in a unit of time. Your counts are frequencies, in cycles/minute. 'Period' means time required for a cycle. Explain how you used your observed frequencies to obtain the periods of the nine pendulums in this experiment.
Your answer (start in the next line):
I constructed my pendulum out of sewing thread and a ring that was metal. The rings mass was probably about .5 pound. The pendulum swung further distance (about 15 in at longest ) when the thread was longer and as the thread shortened in length as the string shortened (approximately 5inches at shortest). A cycle would be when the pendulum moves right to left. I watched the pendulum swing in order to observe the frequency and counted it each time it went to the right side. To obtain the period I divided 60 secs by the number of oscillations each pendulum made.
#$&* explanations with std terminology
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Good work on the revision.
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