{"id":1042,"date":"2017-09-12T02:23:33","date_gmt":"2017-09-11T18:23:33","guid":{"rendered":"http:\/\/people.utm.my\/yap\/?page_id=1042"},"modified":"2017-09-21T17:45:34","modified_gmt":"2017-09-21T09:45:34","slug":"linear-fitting-with-hookes-law","status":"publish","type":"page","link":"https:\/\/people.utm.my\/yap\/linear-fitting-with-hookes-law\/","title":{"rendered":"Linear fitting with\u00a0Hooke’s Law"},"content":{"rendered":"

(Back to index)<\/a><\/p>\n

Assuming that this is the data for a linear experiment with ideally, zero y-intercept:<\/span><\/p>\n

Data<\/h3>\n

Click here to download the data<\/span><\/a>\u00a0or copy the following data into a notepad and save it as a text file.\u00a0<\/span>I normally prefer to change the filetype from “.txt” to “.dat”, simply because, it contains data.<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n
# m (g)<\/span><\/td>\nData 1<\/span><\/td>\nData 2<\/span><\/td>\nData 3<\/span><\/td>\naverage<\/span><\/td>\nstd.dev<\/span><\/td>\n<\/tr>\n
200<\/span><\/td>\n5.683631<\/span><\/td>\n6.29861<\/span><\/td>\n8.381023<\/span><\/td>\n6.787755<\/span><\/td>\n1.413658<\/span><\/td>\n<\/tr>\n
400<\/span><\/td>\n10.23901<\/span><\/td>\n13.5709<\/span><\/td>\n15.18523<\/span><\/td>\n12.99838<\/span><\/td>\n2.522326<\/span><\/td>\n<\/tr>\n
600<\/span><\/td>\n11.84209<\/span><\/td>\n11.36025<\/span><\/td>\n9.422947<\/span><\/td>\n10.8751<\/span><\/td>\n1.280467<\/span><\/td>\n<\/tr>\n
800<\/span><\/td>\n16.33589<\/span><\/td>\n16.92676<\/span><\/td>\n19.82742<\/span><\/td>\n17.69669<\/span><\/td>\n1.868766<\/span><\/td>\n<\/tr>\n
1000<\/span><\/td>\n22.32341<\/span><\/td>\n23.72259<\/span><\/td>\n20.2721<\/span><\/td>\n22.10603<\/span><\/td>\n1.735483<\/span><\/td>\n<\/tr>\n
1200<\/span><\/td>\n24.86626<\/span><\/td>\n27.70103<\/span><\/td>\n28.07837<\/span><\/td>\n26.88189<\/span><\/td>\n1.755747<\/span><\/td>\n<\/tr>\n
1400<\/span><\/td>\n28.19161<\/span><\/td>\n29.78272<\/span><\/td>\n31.26129<\/span><\/td>\n29.74521<\/span><\/td>\n1.535185<\/span><\/td>\n<\/tr>\n
1600<\/span><\/td>\n34.77228<\/span><\/td>\n34.02847<\/span><\/td>\n30.23366<\/span><\/td>\n33.01147<\/span><\/td>\n2.434233<\/span><\/td>\n<\/tr>\n
1800<\/span><\/td>\n37.84083<\/span><\/td>\n38.05711<\/span><\/td>\n36.07914<\/span><\/td>\n37.32569<\/span><\/td>\n1.084949<\/span><\/td>\n<\/tr>\n
2000<\/span><\/td>\n37.64023<\/span><\/td>\n38.79702<\/span><\/td>\n42.7417<\/span><\/td>\n39.72632<\/span><\/td>\n2.674686<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

In this data, the first column is the mass (in grams), hung under a spring.<\/span>
\n The spring extends and the elongation is recorded.<\/span>
\n The experiment is repeated three times to produce three sets of data.<\/span>
\n The average and standard deviation was calculated for these data.<\/span><\/p>\n

Tasks:<\/h3>\n

For this data, we would use the linear equation\u00a0y = mx + c.<\/span>
\n You would need to produce 5 fits and plots to compare the results.<\/span>
\n These are the tasks:<\/span><\/p>\n

    \n
  1. Fit and plot for Data #1 (not the average), where the parameters m and c are fitted (adjusted) to the graph.<\/span><\/li>\n
  2. Fit and plot for Data #1 (not the average), where only parameter m is fitted and parameter c is fixed to zero.<\/span><\/li>\n
  3. Fit and plot for Average Data, where the parameters m and c are fitted (adjusted) to the graph, without\u00a0standard deviation data.<\/span><\/li>\n
  4. Fit and plot for Average Data, where the parameters m and c are fitted (adjusted) to the graph, with\u00a0standard deviation data.<\/span><\/li>\n
  5. Fit and plot for Average Data, where only parameter m is fitted and parameter c is fixed\u00a0to zero\u00a0with standard deviation data.<\/span><\/li>\n<\/ol>\n

    Required Knowledge<\/h3>\n

    To perform the tasks about, one would require the basic knowledge<\/a> of importing data into gnuplot.<\/span><\/p>\n

    Code – Task 1<\/h3>\n

    y1(x) = m1*x + c1<\/span>
    \nm1 = 2<\/span>
    \nc1 = 0.1<\/span>
    \nfit y1(x) ‘data.dat’ using 2:5 via m1,c1<\/span>
    \nplot ‘data.dat’ using 2:5 with points<\/span>
    \nreplot y1(x) with line t “y1(x) : Single Data with y-intercept”<\/span><\/p>\n

    Explanation<\/strong><\/p>\n

    y1(x) = m1*x + c1<\/span><\/p>\n

    First, we would need to define the fitting equation. \u00a0In this case, the fitting equation is a simple linear equation with two variables, m1<\/span> and c1<\/span>.<\/span><\/p>\n

    m1 = 2<\/span>
    \n c1 = 0.1<\/span><\/p>\n

    Then we assign a starting value for m1 and c1. Do not write zero. \u00a0Try to write something within the same order of the actual value. \u00a0The only way to know the actual value to to try to plot the graph without fitting.<\/strong><\/span><\/p>\n

    fit y1(x) ‘data.dat’ using 2:5 via m1,c1<\/span><\/p>\n

    Next, this command fits the y1(x)<\/span> equation with the data ‘data.dat<\/span>‘. \u00a0The command “using 2:5<\/span>” selects only columns 2 and 5 for data-fitting. \u00a0The values which are adjusted are written using “via m1,c1<\/span>” where m1 and c1 will be changed to get the best fit.<\/span><\/p>\n

    plot ‘data.dat’ using 2:5 with points<\/span><\/p>\n

    This command plots the original data with data points<\/p>\n

    replot y1(x) with line title “y1(x) : Single Data with y-intercept”<\/span><\/p>\n

    This command plots the y1(x) equation that has been fitted with a title.<\/p>\n

     <\/p>\n

    (Back to index)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    (Back to index) Assuming that this is the data for a linear experiment with ideally, zero y-intercept: Data Click here to download the data\u00a0or copy the following data into a notepad and save it as a text file.\u00a0I normally prefer to change the filetype from “.txt” to “.dat”, simply because, it contains data. # m […]<\/p>\n","protected":false},"author":14205,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-1042","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/pages\/1042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/users\/14205"}],"replies":[{"embeddable":true,"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/comments?post=1042"}],"version-history":[{"count":0,"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/pages\/1042\/revisions"}],"wp:attachment":[{"href":"https:\/\/people.utm.my\/yap\/wp-json\/wp\/v2\/media?parent=1042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}