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McMaster University Department of Mechanical Engineering ME 3F04 – Modelling and Numerical Solutions Project 1 – Winter 2024 Instructor: Chris Morton (
mortoc5@mcmaster.ca
) Teaching Assistant: Ehsan Majma (
majmae@mcmaster.ca
) Due on:
Feb 9, 5:00pm Submission Location: Hand-written work can be scanned and submitted via A2L dropbox. MatLab codes should be submitted via A2L dropbox. Important Notes: -
Group work is encouraged when solving problems, however each student must submit his/her own work. -
Cheating/plagiarism are forms of academic dishonesty. Such cases (if identified) will follow McMaster Academic Integrity Policy. Students are recommended to review the procedures outlined (particularly in section 6) and understand the consequences. -
Any questions on the grading scheme can be posed to the TA responsible for Project 1 marking. -
Marks will be posted on A2L within 2 weeks of project completion.
Project 1 Question 1 (15 marks).
(This question should be completed by hand) Consider the equation 𝑥 + 𝑒
ି௫
= 2
a) Using the graphical method, determine the number of real roots in the interval −3 ≤ x ≤ 3. Show that one root is near x = 2. b) Apply the direct iteration method to find the root near x = 2 with the following rearrangement
x
e
x
2
First, determine whether iterations will converge and explain briefly. With the rearrangement suggested above, Illustrate the iteration process by completing three
iterations starting with the initial guess of x = 2. Show all intermediate calculations and summarize the results in the following tabular form:
Iteration x
old
x
new
1 2 2 3 c) Apply Newton-Raphson method to find the root near x = 2. Demonstrate the process by completing three
iterations starting with the initial guess of x = 2. Show all intermediate calculations and summarize the results in the following tabular form:
Iteration x
old
f(x
old
) f '
(x
old
) x
new
1 2 2 3 d) Show how to apply relaxation to the iteration process in part c) by completing ONE iteration with the relaxation coefficient ω=0.8 by hand. Briefly explain why under relaxation would usually be applied in an iterative algorithm.
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The following tools / resources may be useful for you to complete the assignment:a. Chatgpt (You may use it to learn Matlab coding or any other computer language. An example is given here: https://shareg.pt/mXHGne9 ). Please take note that code generated by chatgpt can be directly copied and pasted.b. Matlabi) Useful cheat sheet (https://n.ethz.ch/~marcokre/download/ML-CheatSheet.pdf)ii) Getting started with Matlab (https://matlabacademy.mathworks.com/en/details/gettingstarted )iii) Getting 30-day Matlab trial license (https://www.mathworks.com/campaigns/products/trials.html ) iv) Polyfit (https://www.mathworks.com/help/matlab/ref/polyfit.html )v) Exponential Fit (https://www.mathworks.com/matlabcentral/answers/91159-how-do-i-fit-an-exponential-curve-to-my-data)c. PlotDigitizer (https://plotdigitizer.sourceforge.net/ ) or a free online app that does not requires installation (https://plotdigitizer.com/app )You may use your own engineering judgement to make any assumptions on any…
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solve only 'a' part hand written asap
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+ → CO
A student.masteryconnect.com/?iv%3D_n5SY3Pv5S17e01Piby
Gr 8 Sci Bench 1 GradeCam Rutherford TN 2021
AHMAD, ASHNA
D0
3 of 35
A student develops a model of an electric motor using two pins, a wire coil,
coil continues to spin with a certain speed.
wire coil
pins
magnet
tape
battery
How can the student increase the speed of the electric motor?
O by using wider pins
O by using thinner pins
O by using less wire in the clil
O by using more wire in the coil
e Type here to search
近
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est 2 (copy) (page 4 of 9)
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(D Page view A Read aloud V Draw
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© 2013 Pearson Education, Inc.
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(b) What is the tension?
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- The following tools / resources may be useful for you to complete the assignment:a. Chatgpt (You may use it to learn Matlab coding or any other computer language. An example is given here: https://shareg.pt/mXHGne9 ). Please take note that code generated by chatgpt can be directly copied and pasted.b. Matlabi) Useful cheat sheet (https://n.ethz.ch/~marcokre/download/ML-CheatSheet.pdf)ii) Getting started with Matlab (https://matlabacademy.mathworks.com/en/details/gettingstarted )iii) Getting 30-day Matlab trial license (https://www.mathworks.com/campaigns/products/trials.html ) iv) Polyfit (https://www.mathworks.com/help/matlab/ref/polyfit.html )v) Exponential Fit (https://www.mathworks.com/matlabcentral/answers/91159-how-do-i-fit-an-exponential-curve-to-my-data)c. PlotDigitizer (https://plotdigitizer.sourceforge.net/ ) or a free online app that does not requires installation (https://plotdigitizer.com/app )You may use your own engineering judgement to make any assumptions on any…arrow_forwardI need help with the first part and Matlab for this problemarrow_forward4. Documents business requirements use-case narratives.for only one process note: please i want Documents like this in picarrow_forward
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- solve only 'a' part hand written asaparrow_forward+ → CO A student.masteryconnect.com/?iv%3D_n5SY3Pv5S17e01Piby Gr 8 Sci Bench 1 GradeCam Rutherford TN 2021 AHMAD, ASHNA D0 3 of 35 A student develops a model of an electric motor using two pins, a wire coil, coil continues to spin with a certain speed. wire coil pins magnet tape battery How can the student increase the speed of the electric motor? O by using wider pins O by using thinner pins O by using less wire in the clil O by using more wire in the coil e Type here to search 近arrow_forwardHelp solve this USING MATLABarrow_forward
- USE MATLAB AND SOLVE THIS QUESTION The ideal gas law relates the pressure P, volume V, absolute temperature T, and amount of gas n. The law is P = nRT/ V where R is the gas constant. An engineer must design a large natural gas storage tank to be expandable to maintain the pressure constant at 2.2 atm. In December when the temperature is 4°F (- 15°C), the volume of gas in the tank is 28 500 ft3 . What will the volume of the same quantity of gas be in July when the temperature is 88°F (31°C)? (Hint: Use the fact that n, R, and P are constant in this problem. Note also that K =°C +273.2.)arrow_forwardPlz solve within 30min I vill give definitely upvote and vill give positive feedback thank youarrow_forward3. (Make a MatLab code) You have invested money in a bank account that compounds annually. The interest rate is 6.4%. You want to know the balance of the account after 5 years. Use an initial balance of $1000.arrow_forward
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