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Old Nov 4th 2009, 09:06 AM   #1
Nrt
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F-dL Graph Help!

Hi, I need to plot a graph of F=kx for my lab report.

By measuring x, displacement of spring for every mass (20g, 40g,50g) we found k. Now i need to draw F-x graph.

I put my F and x data on graph w/o any problems. But when it comes to draw the line of F=kx i get stuck. Using the line's slope i need to find theoritecal k and calculate the error.

I need to have a graph like this:

http://phoenix.phys.clemson.edu/tuto...h/labgraph.gif

This is my second lab report so i need help to get started and learn how to draw properly.
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Old Nov 4th 2009, 09:17 AM   #2
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i dont know if u are needing this
to find k from F x graph, draw a triangle(anywhere) and of any size with the straight line u have got by plotting F-x as ur hypotenuse and the other sides of ur triangle are parallel to x and y axes.measure these sides with your scale, (convert them to actual values)and take ratio to get tan theta which gives u the slope and hence k.
to find error, take log and differentiate.
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Old Nov 4th 2009, 09:37 AM   #3
Nrt
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Imageshack - adszzx

thanks, but my problem is i dont know how to get my straight line from F=kx. I dont know k so i cant give values and draw.


Is the best fit line that im supposed to draw?
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Old Nov 4th 2009, 10:55 AM   #4
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you draw the line so that it passes through the maximum number of points. also make sure that the number of unused points above this line equals the no of unused points below this line. then find k by my method.
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Old Nov 4th 2009, 11:38 AM   #5
Nrt
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alright, thanks for help.
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Old Nov 4th 2009, 12:11 PM   #6
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Originally Posted by Nrt View Post
Imageshack - adszzx

thanks, but my problem is i dont know how to get my straight line from F=kx. I dont know k so i cant give values and draw.


Is the best fit line that im supposed to draw?
,
Originally Posted by r.samanta
you draw the line so that it passes through the maximum number of points. also make sure that the number of unused points above this line equals the no of unused points below this line. then find k by my method.
I may disagree with r.samanta (depending of the following). One of the most used method for interpolating datas in physics are the least squares method (see http://en.wikipedia.org/wiki/Least_squares or just type it in google and look how to get the equation y=ax+b, where a is the slope. Basically you've found y's and x's, it remains to find out a and b precisely by the Least squares method). Now let me ask you a question Nrt : Have you been introduced to the Least square method? If no, then maybe the tip of r.samanta is good enough. If yes, then you'd have to apply what you've been introduced!
Sidenote : In fact what r.samanta proposed seems something similar to the least square method, but many times the line won't pass by any points. I've made many lab reports and I don't remember a single one in which the line passed by a point I had measured. I even wrote a program (with my friend) in Fortran 90 in order to calculate "a", "b", their errors (or uncertainties) and many more things related to this.

Edit: Maybe take a look at http://www.shodor.org/unchem/math/lls/leastsq.html in order to plot your data to compare with what you did. Search for "linear least squares".
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Last edited by arbolis; Nov 4th 2009 at 12:17 PM.
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Old Nov 4th 2009, 01:53 PM   #7
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Originally Posted by arbolis View Post
,
Nrt : Have you been introduced to the Least square method? If no, then maybe the tip of r.samanta is good enough. If yes, then you'd have to apply what you've been introduced!

Edit: Maybe take a look at Linear Least Squares Regression in order to plot your data to compare with what you did. Search for "linear least squares".
They showed advanced methods like least square, regression but told us that we don't have to use it on our reports.

I think r.samanta was talking about this:










So, that is the way i've done it.

Also, i've tried to use your link but it says:

Error: Lists do not contain expected number of data points. Check the number of data points in the lists against the number in the top field.
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Old Nov 4th 2009, 02:04 PM   #8
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Your graphic looks good.
I tried some points in http://www.shodor.org/cgi-bin/cchem/leastsq.pl and all worked fine. It seems you entered wrongly the number of points you have or you forgot a to enter a data in the table. If the number of points coincide with what you entered then all should work fine in my opinion.
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Old Nov 4th 2009, 04:20 PM   #9
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Thanks for help. I'm about to finish my work. I think i'll have time to sleep :P.
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Old Nov 4th 2009, 04:27 PM   #10
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Originally Posted by Nrt View Post
Thanks for help. I'm about to finish my work. I think i'll have time to sleep :P.
Glad to know we've helped you. Good luck with your work.
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