Working with Spreadsheet

Introduction:
The lab's main purpose is to familiaize ourselves and learn new techniques for using the electronic spreadsheet.

Procedure:

• Using Microsoft Exel create a spreadsheet that calculates the values of the function f(x)=Asin(Bx+C) using the following values: A= 5, B = 3, C =  π/3. These values are the constants and should be labeled with amplitude, frequency, and phase. Make a colum for 'x' and one for 'f(x)'; for the first x value enter a zero and for f(x) enter the given formula. The x colum should run from 0 to 10 with an incriment of 0.1 radians. Using the formula have the spreadsheet calculate the all x values by dragging the select box from the cell with the formula to the last cell (Figure 1).
• Copy the calculated values and after loading the graphical analysis application paste the data on to the program. This should show the graph for the value (name the axis).
• Select a portion of the graph to be analyze and find the best curve fit that fits the function (sin function). After the functions has been fit a box displays a value for A, B, and C that fit the plotted graph. These values that are displayed on the box should match the constant values that were assigned to the function (Figure 2).  
• Repeat the above process to calculate the position vs time values of a free falling object. The constants for the function are g = 9.8 m/s^2, Vo = 50 m/s, and Xo = 1000m and change in time t = 0.2. Analyze the graph and curve fit it to a quadratic function (Figure 3). 

 Figure 1

On the left, the table for the sine function is shown. The right side shows the position vs time values for a free-falling particle. 

 Figure 2

The selected portion of the graph was analyzed and the curve fit was a sine function. The values given by the curve fit are the same as the constant values of the original function.

   Figure 3

Position vs Time graph for a particle with an initial position of 1000m

Conclusion:
The lab was excellent practice for using spreadsheets to calculate values for a given function. Using the spreadsheet is a great method to calculate since one can plug the formula, constant values, and solve for x. For example, on the first portion of the lab we have function, the x values (0-10 incrementing by 0.1), and by saving the constants on the formula and dragging the select box down all the values are calculated by Excel. An experimental error which we came across was that our free falling particle graph was showing a different graph because on the process of calculating we got stuck on a loop that would only calculate 3 values repeatably. We solved the issue by re-assigning the constants and incrementing our time once more.After we curve fit our data using the quadratic equation since it was the closest to the graph we obtained. The value A represents the initial position of the object, B represents velocity, and C is half of gravity.