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# Summary - Summary Phys 211L Spring 2010 FINAL GRADE 87 Note...

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Summary - Phys 211L Spring 2010 FINAL GRADE : 87 Note: I found Phys211L as a very ugly course for all the semester, I was used to do NOTHING to prepare the class. 3 days before the final I began to study and did this summary that was quite helpful… In fact, the best way to study phys211L is to follow in class (spending 15 minutes before the lab reading and printing the manual) and the most important is to understand the calculations of errors (linear regression, propagation of errors) !! Done by Erik VZ (you can add me on facebook, if you have any question to ask me do not hesitate) Please check out the following website!! http://4greeneraub.blogspot.com/ (about environmental issues) If you are interested, join its page on Facebook, named For a Greener AUB

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Preparation for final of 211L There might be errors; it’s only kind of a summary of the labs ERRORS 1- Linear Regression (finding the slope + error on the slope) Many experiments yield a series of pairs of data values. Usually the x i values are selected and the y i values are measured. A graph is plotted with each pair (x i ,y i ) representing a point. If the points of the graph are located within a narrow band, the variables x and y are said to be correlated, and a relation exists between x and y. (we write the formula under this form and we decide of x and y) y = Ax + B We enter on the calculator: linear regression, x,y M+ Shift 2 We take the value of r (correlation coefficient which should be equal to 1 or - 1) The value of A which is the y intercept (B in our formula) The value of B which is the slope (A in our formula) Y= slope*X + y intercept e i = y – y i = Ax i + B – y i 2 2 ) ( = i i x x N The error is : = 2 2 2 i A e N N σ (don’t forget to do the root square) WE DRAW A TABLE Y i X i X i 2 e i e i 2 Sum yes yes no yes 2- Propagation of error In order to estimate the error in compound quantities , the following procedure is followed. If a number of measured quantities have arithmetic means x, y,
and z with root-mean-square errors of α x , α y , and α z respectively, then the root-mean-square error α F in any function F of x, y, and z is given by 2 2 2 ) ( ) ( ) ( z y x F z F y F x F α + + = 3- Errors of observation Several measurements for the same thing. For example we measure 10 times the length of a rod. Average: N x x i = Deviation: x x d i i = Root mean square error: ) ( 1 2 = N N d i DRAW A TABLE x i d i d i 2 Sum No Yes In this course, the quantity α should be rounded to one significant figure only (or two sometimes). Note that the least significant figure in the result should be of the same order of magnitude as the uncertainty. Very often in the process of calculations extra figures are accumulated and sometimes reported in the end result. This is a meaningless procedure . No figures should be included beyond the precision of the original data.

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Summary - Summary Phys 211L Spring 2010 FINAL GRADE 87 Note...

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