• x = 5 (not -5)
• The video demonstration can be very helpful if you have not used Excel much before.
• Use Excel to tabulate each series where each row adds a new x term to each series. Use column A to hold the term number "n" which is the power of the x term, starting with n=0.
• Use 26 terms from n=0 to n=25 (not 25 terms from n=0 to n=24).
• The Excel function FACT(number) can be used to calculate the factorials.
• In the first series, (-1)^n can be used to create the appropriate sign for each term.
• Use the Excel function EXP to calculate the true value for the error calculations.
• Calculate the series values and relative percent errors ε_t and ε_a for each number of x terms from 1 to 25 (not just for n=25, for which the answers are provided below).
• Include printouts of your tabulated series (with row numbers and column letters visible, using the Page Layout - Sheet Options tab) and write out or print the Excel formulas (with cell references) used for each column (e.g., from the n=1 row of your calculations). The easiest way to do this is to copy and paste the formulas into an Excel text block or a Word document, and add a cell label for each formula (e.g., "A1: = formula in cell A1").
• For n=25 (26 terms including the 0 term),
  • series1 = 0.006737944   (|ε_t| = 4.6 x 10^-5%, ε_a = -2.9 x 10^-4%)
  • series2 = 0.006737947   (|ε_t| = 3.0 x 10^-9%, ε_a = -1.3 x 10^-8%)
• Comment on the differences between the results for the two approaches.

• Be sure to chop off (i.e., truncate, don't round) the "digits" (not decimal places), not counting any leading zeroes
• Chop after each sub calculation (i.e., after each arithmetic step: exponentiation, multiplication, addition, subtraction).
• Using 3 digits, f' = 216,000 (calcs and answer chopped to 3 digits)
• Using 4 digits, f' = 2,048,000 (calcs and answer chopped to 4 digits)
• Comment on the results.

• For second order, f = 354,  |ε_t| = 36.1%

• Calculate |ε_t| for each result.
• Ignore the last sentence.
• No answers are provided.

NOTE - this problem is not in the book or on the website. The background and equations you need to solve this problem will be presented in class.

Spreadsheet transmission analysis:

Using Excel, create a spreadsheet to perform the analysis of a 3-speed transmission. All of the necessary equations will be presented in class. Use the spreadsheet to process each of the following cases:
 

 
where P is the gear diametral pitch, c is the shaft centerline distance, the N's are the number of teeth on the indicated gears, and 1st-to-2nd and 2nd-to-3rd are the car speeds at which the transmission is shifted.

You must provide:

• A listing of the Excel formula expressions used for each of the cells listed below. The term "c/p" below means copy and paste. The formula must be in a form that is can be copied as is and pasted to the indicated cells, and not require any additional editing.
• A14 (c/p to B14, C14, and A21:C21).
• A19 (c/p to B19, C19).
• A26 (c/p to B26).
• A34 (c/p to B34).
• A39 (c/p to A40:A73).
• B38 (c/p to B39:B73).
• C38 (c/p to C39:C73).
• D38 (c/p to D39:D73).
• C75.

Note:

• The formula expressions used must be general enough so they work for any input parameters without editing the formulas. In other words, the formulas should be the same for all three design-variable cases.
• Excel offers the function PI() to report a precise value for π. This can make some of your formulas more concise, more accurate, and easier to read.
• In cells C38 and D38, you will need to use the Excel function: IF().  You might want to look it up in the Excel help system for more info.  Also, here's a link to a good example of how it is used: MECH102 grades Excel example (see cell U9, which assigns a letter grade automatically). In the transmission problem, you need to compare the drive-shaft speed to the drive-shaft shift speeds to determine which "gear" you are in.
• The easiest way to provide the list of formulas in a concise and readable way is to copy and paste them into a Word document. Be sure to precede each formula with its cell label (e.g., "A14: = formula in cell A14").
• To create the "engine speed" vs. "car speed" plot, select both columns of data, using the Ctrl key to add the 2nd column to the selection. Then select Scatter Plot (XY plot with straight lines and markers) on the Insert - Charts tab. If you want to change plot formatting, right click on the thing you want to change (plot area, curve, axis, or legend) and select the relevant menu item.

• A printout of the spreadsheet results (including the graph) for each of the three cases listed above. Be sure to include grid lines and column and row headings ("A, B, C, ..." and "1, 2, 3, ...") on each printout (see the Page Layout - Sheet Options tab).

Your spreadsheet printouts should look like the example provided. The row and columns numbers for each formula cell must match those in the example.