Recovering from the arduous task of measuring rice that we did the last two meetings, we were thrust to a new topic which was graphical analysis.
Graphical analysis is basically understanding the relationship between two or more quantities displayed in graphical form. Bar graphs and pie charts were discussed as graphs that are used to show the distribution of a particular set of data. Scatter plots are graphs that show how one quantity changes as the independent quantity is changed. This could be explicitly presented as a function.
The elements of the scatterplot (the ind. and dependent variables, error bars, and the line of best fit) were also discussed. We were also taught how to graph scatter plots in Microsoft Excel, and how to implement error bars and best fit lines in our graphs.
Linearization was also discussed. The idea of this topic is to express higher order functions as linear functions, or functions of the form mx+b because linear forms are generally easier to handle and it is very easy to see the relationship of variables and constants with this form.
Getting back to our activities for the day, we didn't really get a chance to directly implement the things that we learned because we unfortunately didn't bring a laptop for our group. Thus, we were reduced to go to another group and observe. The first line of business was to plot a set of data given x, y, and uncertainty in x. The plots to done were x vs y, x^2 vs y and x^3 vs y. Admittedly, I think that I am very proficient in making spreadsheets in MS Excel, but I learned that day that I lacked knowledge in graphing in Excel. After this, the line of best fit and error bars were applied.
Another set of data were to be graphed after that. This set of data involved the moment of inertia and distance. The formula for the moment of inertia is:
I= I(cm) + md^2,
we were tasked to find m and I(cm).
We applied linearization to the equation by plotting d^2 as x, and I as y, getting the linear form of y=mx+I(cm). In this, the slope of the line is the mass, while the y-intercept (or constant) is the I(cm).
After this, we started the activity that we would perform next week- taking the time it takes for a small cart to get to the other side by applying a constant force.
This lab meeting was a jam-packed day. Unfortunately, we didn't really get the chance to make the most out of the lessons because of our lack of laptop. There were certain times today that I got bored, not because the things that we did were boring, but because of the aforementioned problem.
Almost everything that we learned this lab meeting was new to me, most notably the error bars and line of best fit. Linearization also appealed to me as a very interesting topic. I plan to experiment with MS Excel to better understand scatter plots and linearization.