The purpose of this lab was to become familiar with electronic spreadsheets by using them in some simple applications by the use of a computer with Excel software.
We were given the values of A =5, B =3, and C = π/3. We placed the values on the left side of the
spreadsheet and labeled them with amplitude, frequency, and phase as an explanation for the meaning of
each constant. We also made a column for "x" and "f(x)" with "x" being in increments of 0.1 radians and
"f(x)" being this formula:
f(x) = A sin(Bx + C)
With those given values, increments, and formula, we were able to come up with Table #1, and also one that
shows exactly how we applied the formula to the software using the different columns and rows:
Once we were sure all the data was input correctly, we copied and pasted the data onto the Graphical analysis software. A graph of the data appeared and was labeled with correct vertical and horizontal axes. We then directed the computer to find a function that best fits the data which was the same that was used to find "f(x)." The graph was in the form of sin(x):
The values that were given by the computer by using the function that best matched the data, gave the same exact numbers that were used in the spreadsheet to find what "f(x) was equal to. A was equal to 5, B was equal to 3, and C was equal to π/3. The graph had the same amplitude, frequency and phase.
After that first spreadsheet was completed, we repeated the process for a spreadsheet that calculates the position
of a freely falling particle as a function of time. The constants that were included were acceleration of gravity,
the initial velocity, initial position, and the time increment. G = 9.8 m/s^2, v0 =50 m/s, x0 = 1000 m, and Δt = 0.2s. We put our constants on the left side and had two columns of "x" and "f(x)" where we used the quadratic formula:
f(x) = A + Bx + Cx^2
and found how much the particle had fallen for every 0.2 s:
A data table for Data Table #2 was also made that shows how the columns and rows were used for the software to make the calculations for us:
After the data was checked, and was accurate to the constants we were given for the calculations, we copied and pasted column "x" and "f(x)" onto the Graphical Analysis software and labeled the horizontal x-axis and vertical y-axis. The software gave us the shape of a concave up parabola that started from 1000 m, traveled up about 63 m, and them came falling down with an acceleration of 9.8 m/s^2 to 0 m. We then had the computer find a function that best fit the curve which came out the be the quadratic formula that was also used to calculate the data:
The values that the computer gave us for A, B, and C were the same that we had been given from the beginning. The particle had been thrown with an initial velocity of 50 m/s at 1000 m high with a constant acceleration of 9.8 m/s^2. The data that was calculated in the spreadsheet was the same as the data that the Graphical Analysis calculated.
The lab demonstrated how data can be more precisely gathered by the use of software that accurately does calculations. It taught how to input data into Excel, and giving it functions that will use the data you input to solve for whatever is being sought. The lab didn't bring up many sources of error since the software in the computer held the task of doing the calculations. The only error that could have happened could be a slightly small human error in that input of data could have been written wrong or not paired up correctly into the functions. A further thing that the lab could teach is finding derivatives of functions that would help find out how the position vs. time, velocity vs. time, or acceleration vs. time graph would look.
