Calculating Velocity The velocity is calculated by entering the following: =(B3-B2) / (A3-A2). Then drag the box in the lower right corner of the cell down to calculate other values. Note that there must be one fewer velocity value than position value.
Useful Excel Functions = SUM(A1:A10) — calculates the sum of the data in cells A1 to A10 = AVERAGE(A1:A10) — calculates the average of the data in cells A1 to A10 = STDEV(A1:A10) — calculates the standard deviation of the data in cells A1 to A10 = SQRT(A1) — square root of number in cell A1. = ROUND(A1,3) — rounds the number in cell A1 to three significant digits. =ABS(A1) — absolute value of the number in cell A1.
Excel’s Trig Functions You are likely to use SIN(A1), COS(A1), ASIN(A1) and ACOS(A1) Trig functions in Excel assume the argument is in radians. = Radians(A1)– assumes that the value in cell A1 is an angular measurement in degrees and converts it into radians. =SIN(RADIANS(A1)) – converts the value in cell A1 into radians and then takes the sine of it.
Least Squares Fitting The least squares fitting method minimizes the sum of the squares of the differences between the data points and a theory curve When working with linear data, the lab manual often asks you to insert a trendline and then do a linear regression The difference between the two operations in Excel is that the trendline plots the theory line on your graph the linear regression gives the uncertainties in the fit parameters. You will want to do both
Linear Regression In Excel, to do a linear regression you must have selected a cell, not a graph In Excel, the Data Analysis Tools must be installed Select “Tools>Data Analysis>Regression Slope Uncertainties Intercept
Graphs Plot experimental data as points or points with error bars Plot theory as continuous lines—usually this is done using the “trendline” feature To add error bars, double click on a data point and select X or Y error bars. (Do this before you add a trendline.) Trendlines can be linear, logarithmic, polynomial, power, exponential or a moving average. When adding trendlines, select the options to display equation and R 2. The equation of the trendline gives the fit parameters. R 2 is a measure of the goodness of fit and R 2 =1 is optimal.
Graphs Equation of trendline — note that parameters are the same as linear regression on previous slide.