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PHY 201
Your 'timer program' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** TIMER program_labelMessages **
2-18 4pm
** **
1 hour
** **
Operating the TIMER program
It is easy to operate the Timer program. All you have to do is click on the button labeled Click to Time Event.
Click that button about 10 times and describe what you see.
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Now click on Initialize Counter, which will clear all the data from the timer window. Click the mouse as fast as you can until the TIMER window fills up. Be sure you get at least 20 time intervals.
If you miss a click, try again. Keep trying until you get at least 20 quick-click intervals without a missed or delayed click.
Copy your data starting in the next line:
1 .21875 .21875
2 .359375 .140625
3 .515625 .15625
4 .703125 .1875
5 .859375 .15625
6 1 .140625
7 1.15625 .15625
8 1.3125 .15625
9 1.5 .1875
10 1.671875 .171875
11 1.84375 .171875
12 2 .15625
13 2.203125 .203125
14 2.375 .171875
15 2.53125 .15625
16 2.703125 .171875
17 2.875 .171875
18 3.03125 .15625
19 3.1875 .15625
20 3.34375 .15625
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You got at least 20 time intervals. Based on your data what was the average of the first 20 time intervals? Note that you could get this average by averaging the first 20 intervals. My first few intervals were .15625, .15625, .1875, .171875, etc; I could just add up the first 20 intervals and divide by 20 to get the average. However there is an easier and quicker way to get the result, so use the easier way if you can. NOTE: Spreadsheet calculations and other methods that disguise the process of finding the average are not valid answers to this question. Spreadsheets are perfectly legal for most data analysis, but not in this experiment.
Give your result, number only, in the first line, and starting in the second line explain how you got it.
average of quick-click intervals:
.1671875
explanation:
Instad of adding all of the intervals together and dividing to find the average, I used to total time as it was equivalent to the intervals added together. 3.34375/20=.1671875
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That is the most appropriate way, with this data, to get the result.
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However your first interval appears to be a slight anomaly. I don't believe it really represents a valid quick-click interval, so it would have been a good idea to do just a few more clicks (as you might well have done) and count the data between the second and 21st click.
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When I did this activity the first few lines of my data were as follows:
event number
clock time
time interval
1
11.67188
11.67188
2
11.875
0.203125
3
12.0625
0.1875
4
12.20313
0.140625
5
12.375
0.171875
6
12.54688
0.171875
7
12.73438
0.1875
8
12.92188
0.1875
9
13.10938
0.1875
10
13.28125
0.171875
11
13.4375
0.15625
It looks like the same intervals keep popping up. For example .1875 seconds occurs 5 times out of the first 10 intervals, .171875 seconds occurs three times, and .203125 seconds, .140625 seconds and .15625 seconds each occur once.
A frequency distribution for my time intervals would be as follows:
time interval
frequency
,140625
1
.15625
1
.171875
3
.1875
5
.203125
1
What different time intervals did you observe in your first 20 intervals, and how many times did each occur? List below the different time intervals you observed and the number of times each occurred. List from the shortest to the longest interval, and use a comma between the time interval and its frequency. For example my data above would be listed at
.140625, 1
.1565, 1
.171875, 3
.1875, 5
.203125, 1
The above list is called a frequency distribution. Be sure you make note of this terminology.
Your list should be in exactly the above format, with no other symbols or characters.
Your list (i.e., your frequency distribution):
.140625, 2
.15625, 9
171875, 5
.1875, 1
.203125, 1
.21875, 1
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You are welcome make any comments or ask any question about the process so far.
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On the 10 intervals I've shown you, do you really think I managed to get a time of .1875 seconds, accurate to 4 significant figures, on half of the intervals? If you do, I'm grateful for your confidence but I'm just not that good. No human being has that much neurological and muscular control.
So why do you think the TIMER program reported that time so frequently? Why weren't there times like .1830 seconds, or .1769 seconds? Does this mean that the TIMER program is flawed? Does that mean it's useless?
Why did the TIMER report .1875 seconds multiple times; your conclusions about the program:
The computer runs on its own timing system. The time between one cpu cycle and that of real time is slightly different. Over a longer period of time the timing is less and less flawed. But while measuring in milliseconds the computer could be seen as useless.
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Good.
The interval, incidentally, turns out to be 1/64 second.
The version of the TIMER you used might or might not be the same as the version that created the data given here.
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Here are a few more lines of data, with an added column showing the difference between each time interval and the next.
clock time
time interval
difference from one time interval to next
9
13.10938
0.1875
-0.01563
10
13.28125
0.171875
-0.01563
11
13.4375
0.15625
0.03125
12
13.625
0.1875
-0.01563
13
13.79688
0.171875
0.015625
14
13.98438
0.1875
0.015625
15
14.1875
0.203125
-0.03125
16
14.35938
0.171875
-0.01563
17
14.51563
0.15625
0.03125
Take a good look at that last column and tell us what you see in those numbers, and what this tells you about the TIMER program:
First of all I noticed that you rounded up every time a number ends in 3. Second I noticed that .015625 is half of .03125.
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Note that .015625 is 1/64.
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Now initialize the TIMER once more, and take a series of 10 relaxed breaths. Every time you start to inhale, hit the TIMER button.
My results for the first 7 complete breaths are as follows:
series of relaxed breaths
event number
clock time
time interval
difference between time interval and next
1
1569.734
1569.734
2
1582.75
13.01563
0.32812
3
1596.094
13.34375
3.90625
4
1613.344
17.25
2.70313
5
1633.297
19.95313
1.35937
6
1654.609
21.3125
4.23438
7
1680.156
25.54688
2.15625
8
1707.859
27.70313
I didn't go on because the time between my breaths kept increasing, and I was afraid if I relaxed any more I might stop breathing altogether. It's going to take either more statistical analysis to determine whether that's a real danger, or a little common sense.
Report your results by just entering your time intervals, one to each line, in the box below. If I was entering my results I would enter
13.01563
13.34375
17.25
19.95313
21.3125
etc.
Enter your results in the same format:
3.75
3.1875
3.734375
3.675781
3.46875
3.65625
3.6875
3.5625
3.597656
3.375
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If you have any comments please insert them here
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Most likely you did not observe the same exact time interval twice, and if you did it did not happen nearly as often as when you did the fact clicks.
Why do you think this is exactly what we would expect?
I think that we were clicking faster than the cycles of the timer program could complete different cycles which made it seem as if we were clicking at the exact same times. When breathing we allowed the timer program to complete it’s cycles uninterrupted allowing for more accurate readings.
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Which of the following statements do you think is the most accurate?
a. The TIMER program is capable of determining the time between two events accurately to within about .1 second.
b. The TIMER program is capable of determining the time between two events accurately to within about .01 second.
c. The TIMER program is capable of determining the time between two events accurately to within about .001 second.
d. The TIMER program is capable of determining the time between two events accurately to within about .0001 second.
Enter your answer and your reasoning below:
B.One of the numbers I got from the previous example was 3.75. This is the number with the least amount of decimal numbers. Many of the other numbers go to .00001 but, I believe that those are inaccurate.
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Good.
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*#&!
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The 1/64 second interval tells us that the program is accurate to within about .015 sec, close to .01 sec.
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*#&!
&#Good responses on this lab exercise. See my notes and let me know if you have questions.
Revision isn't requested, but if you do choose to submit revisions, clarifications or questions, please insert them into a copy of this document, and mark your insertions with &&&& (please mark each insertion at the beginning and at the end).
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