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MANE 3351 - Manufacturing Engineering Analysis

Laboratory 8 Assignment

Assigned: November 12, 2025

Due: November 19, 2025 (before 9:30 AM)

Learning Goals

  1. Utilize graphical analysis to determine starting points for bracketed and non-bracketed root finding methods, and
  2. Implement a bracketed and non-bracketed root finding method of your choice.

Description

A general equation for cutting force calibration is given by \(f(x)=ae^{bx}-F_c\). For a specific application, the root of the equation specified below

\[ f(x)=500e^{0.1x}-1000 \]

where \(x\) is the cutting speed and \(x\) is bracketed on the interval \([5,10]\) must be found.

Step 1

Edit the first cell (markdown), to update your personal information for laboratory 8.

Step 2

In cell two, complete the following steps:

  • Create a user-defined function for equation provided in the description above,
  • Vectorize the user-defined function,
  • Create an array for the x-values on the interval of [5,10] that contains at least 100 points,
  • Create an array for the y-values using the vectorized function that contains the values of the vectorized x-values,
  • Use Matplotlib to create an x-y graph, and
  • Verify that the cutting speed values of 5 and 10 provide a bracket of the root of the equation.

Step 3

In cell three, implement one of the bracketed root finding methods using the start values found in step two to find the root with a tolerance of 10^-5. Your code in cell three should print the value of the root.

Step 4

In cell four, implement one of the non-bracketed root find methods for the function described in the description. Use one (or both) of the bracketing value(s) verified in step 2 as the starting value(s). Find the root with a tolerance of 10^-5. Your code in cell three should print the value of the root.

Step 5

After running and testing your program, save the Jupyter Notebook. Upload your repository using GitHub desktop.