It would be good if you had all the data, but it's possible to do a good analysis of this data set.
I believe that the given data can be used to infer what would happen to a pendulum starting from the 30 cm amplitude. It would take something a little over 60 seconds for the amplitude to decrease to 10 cm, another 20 seconds or so to decrease to 7.5 cm, a bit more than an additional 20 seconds to decrease to 5 cm, and another 50 seconds or so to decrease to 2.5 cm.
It would therore be possible to graph amplitude vs. clock time, sketch a smooth curve and report various properties.
To be safe you'll want your instructions to the analyzer to be very specific about what it means to graph amplitude vs. clock time. There is a tendency to confuse time intervals with clock times.
The graph will look a lot like a decreasing exponential function, asymptotically approaching the horizontal axis.
It isn't hard to test whether the graph is exponential:
The graph is exponential if the 'half-life' is constant. The 'half-life' is the time required for the amplitude to decrease by half. For example, that would be the time required to decrease from 30 cm to 15 cm, or from 10 cm to 5 cm, or from 20 cm to 10 cm, etc..
I would suggest asking your analyzer to make her best estimates of the time required for the amplitude to fall to half, starting from at least five different points spread out more or less uniformly over the graph.
You will also want to ask for table indicating a good series of points on her curve. That will allow a reader to evaluate her consistency in sketching a good curve and estimating coordinates of points.
A large and carefully ruled graph will give better results so you might suggest that. Graph paper would be the easiest thing to use (the default paper at http://www.printfreegraphpaper.com/ has a 1/4-inch grid, which would work well), provided your analyzer has a printer available.
I estimate that the positions 30 cm, 10 cm, 7.5 cm, 5.0 cm and 2.5 cm occur at clock times 0, 63 sec, 82 sec, 104 sec, and 158 sec. You might make a quick hand sketch of this graph for reference as you write your instructions for the analyzer.
It seems obvious to me that the 'half-lives' are decrease as you start from lesser and lesser amplitudes. This is what I would expect. I wouldn't share this expectation with your analyzer; this will be a question for the interpreter.
These are just suggestions. You can put your own twist on them, and ask any related or unrelated questions you choose.
It would be best to run a draft by me before sending it to your analyzer.
--------------------------------------------------------------------------------
From:
Sent: Tuesday, December 04, 2012 9:37 PM
To: David Smith
Subject: Fwd: Supervised Study Fall 12: Group 1 Analysis
Professor Smith,
These are the results that Ernest got from the trials he ran for our Group 1 Experiment.
He does not have all the timing data.
He said he would rerun the trials but I think he's gotten bogged down with work and I haven't heard from him lately.
Do you think we can work with what we have here?
Thanks,
sump
#$&*
Your 'orientation part v' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** Orientation Part V_labelMessages **
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Jeremy,
This looks very good. I like a lot of your wording, especially regarding the idea of the timeline.
A few simple editing comments:
the clock time to get from 30 seconds to 7.5 seconds would be 70 seconds
should read
the clock time to get from 30 centimeters to 7.5 centimeters would be 70 seconds
Your sentence
Show your timeline in comma delimited form up to the decay to 2.5cm amplitude
would probably be clearer if you eliminated up to the decay. The sentence
Show your timeline in comma delimited form up to 2.5cm amplitude
seems to make your meaning clear.
I would change
default paper
to
default graph paper
and also mention that the analyzer can construct his or her own graph on any paper, as long as it's accurately and carefully constructed, but that the graph paper might be more convenient.
Describe the line
should probably read
Describe the line or curve
start at one of the following amplitudes to decay to half
seems to indicate that only one amplitude should be picked. I would suggest
start at each of the following amplitudes to decay to half.
Make the changes you choose to make, as you choose to make them, after which you're ready to send this on.
From: sump
Sent: Wednesday, December 05, 2012 10:40 PM
To: David Smith
Subject: Re: Supervised Study Fall 12: Group 1 Analysis
Here is what I propose:
1. For each amplitude decay segment (e.g. 30 cm to 10 cm) find the mean of the two trials.
2. Using the mean for each amplitude decay segment construct a timeline as if each segment was part of one continuing trial.
For example if the decay segment from 30cm to 10 cm took 50 seconds and the segment from 10 to 7.5 took 20 seconds, the clock time to get from 30 seconds to 7.5 seconds would be 70 seconds.
You could show this in comma delimited form as
50 sec, 10cm
70 sec, 7.5 cm
Show your timeline in comma delimited form up to the decay to 2.5cm amplitude.
3. Plot a graph of amplitude vs. clock time.( If you have a printer, you can use the default paper at http://www.printfreegraphpaper.com/ . The 1/4-inch grid would work well). Be careful and make sure the graph show the time that would have elapsed if all of the trials were part of one continuing trial. ( to clarify, in the example above the clock time when the amplitude decays to 7.5cm would be 70 seconds)
4. Does the graph suggest a linear function or a smooth curve?
5. Describe the line.
6. Based on the graph give estimates of what you would expect the time interval it would take for a start at one of the following amplitudes to decay to half of that amplitude (e.g for 30cm, what would be the time interval to decay to 15cm): 30cm, 25cm, 20cm, 15cm, 10 cm.
Give you answers in five lines in comma delimited form first the starting amplitude and then the time interval.
Thanks for your help.
Jeremy
PHY 121
On Tue, Dec 4, 2012 at 10:05 PM, David Smith wrote:
Jeremy,
It would be good if you had all the data, but it's possible to do a good analysis of this data set.
I believe that the given data can be used to infer what would happen to a pendulum starting from the 30 cm amplitude. It would take something a little over 60 seconds for the amplitude to decrease to 10 cm, another 20 seconds or so to decrease to 7.5 cm, a bit more than an additional 20 seconds to decrease to 5 cm, and another 50 seconds or so to decrease to 2.5 cm.
It would therore be possible to graph amplitude vs. clock time, sketch a smooth curve and report various properties.
To be safe you'll want your instructions to the analyzer to be very specific about what it means to graph amplitude vs. clock time. There is a tendency to confuse time intervals with clock times.
The graph will look a lot like a decreasing exponential function, asymptotically approaching the horizontal axis.
It isn't hard to test whether the graph is exponential:
The graph is exponential if the 'half-life' is constant. The 'half-life' is the time required for the amplitude to decrease by half. For example, that would be the time required to decrease from 30 cm to 15 cm, or from 10 cm to 5 cm, or from 20 cm to 10 cm, etc..
I would suggest asking your analyzer to make her best estimates of the time required for the amplitude to fall to half, starting from at least five different points spread out more or less uniformly over the graph.
You will also want to ask for table indicating a good series of points on her curve. That will allow a reader to evaluate her consistency in sketching a good curve and estimating coordinates of points.
A large and carefully ruled graph will give better results so you might suggest that. Graph paper would be the easiest thing to use (the default paper at http://www.printfreegraphpaper.com/ has a 1/4-inch grid, which would work well), provided your analyzer has a printer available.
I estimate that the positions 30 cm, 10 cm, 7.5 cm, 5.0 cm and 2.5 cm occur at clock times 0, 63 sec, 82 sec, 104 sec, and 158 sec. You might make a quick hand sketch of this graph for reference as you write your instructions for the analyzer.
It seems obvious to me that the 'half-lives' are decrease as you start from lesser and lesser amplitudes. This is what I would expect. I wouldn't share this expectation with your analyzer; this will be a question for the interpreter.
These are just suggestions. You can put your own twist on them, and ask any related or unrelated questions you choose.
It would be best to run a draft by me before sending it to your analyzer.
________________________________
From: sump
Sent: Tuesday, December 04, 2012 9:37 PM
To: David Smith
Subject: Fwd: Supervised Study Fall 12: Group 1 Analysis
Professor Smith,
These are the results that Ernest got from the trials he ran for our Group 1 Experiment.
He does not have all the timing data.
He said he would rerun the trials but I think he's gotten bogged down with work and I haven't heard from him lately.
Do you think we can work with what we have here?
Thanks,
sump
Phy 121 (Group 1)
---------- Forwarded message ----------
From: leo
Date: Wed, Nov 28, 2012 at 4:35 PM
Subject: Re: Supervised Study Fall 12: Group 1 Analysis
To: sump
10 cm starting amplitude
test 1 20.83594
test 2 17.23438
7.5 cm starting amplitude
test 1 23.03906
test 2 21.13672
5.0 cm starting amplitude
test 1 54.03516
test 2 52.85938
30 cm starting amplitude
test 1 65.82422
test 2 61.07422
These are the results i did practice runs first to help perfect it and took down data for two tests of each.