ENGR 328 Computational Methods in Engineering

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Wbar111

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i need you to answer the questions on MATLAB i just need the code of it

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1. Write an M-file that uses the bisection method to determine the drag coefficient needed so that an 95-kg bungee jumper has a velocity of 46 m/s after 9 s of free fall. Note: The acceleration of gravity is 9.81 m/s2. Start with initial guesses of xl = 0.2 and xu = 0.5 and iterate until the approximate relative error falls below 5%. The following is an equation describing the relationship between velocity, mass, gravity, the drag coefficient, and time:

2. Determine the positive real root of ln(x2 ) = 0.7

(a) graphically

(b) using three iterations of the bisection method, with initial guesses of xl = 0.5 and xu = 2

(c) using three iterations of the false-position method, with the same initial guesses as in (b)

3. Write an M-file to employ fixed-point iteration to locate the root of

Use an initial guess of x0 = 0.5 and iterate until ?a ? 0.01%. Verify that the process is linearly convergent as described in the class slides.

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ENGR 328 Homework 4 Due: 02/14/2019 @ 2:00 pm Please upload a PDF of your homework including generated plots and any .m files you created. 1. Write an M-file that uses the bisection method to determine the drag coefficient needed so that an 95-kg bungee jumper has a velocity of 46 m/s after 9 s of free fall. Note: The acceleration of gravity is 9.81 m/s2. Start with initial guesses of xl = 0.2 and xu = 0.5 and iterate until the approximate relative error falls below 5%. The following is an equation describing the relationship between velocity, mass, gravity, the drag coefficient, and time: 2. Determine the positive real root of ln(x2) = 0.7 (a) graphically (b) using three iterations of the bisection method, with initial guesses of xl = 0.5 and xu = 2 (c) using three iterations of the false-position method, with the same initial guesses as in (b) 3. Write an M-file to employ fixed-point iteration to locate the root of Use an initial guess of x0 = 0.5 and iterate until εa ≤ 0.01%. Verify that the process is linearly convergent as described in the class slides. 4. Determine the highest real root of f(x) = x3 − 6x2 + 11x − 6.1: (a) Graphically (b) Using the Newton-Raphson method (three iterations, x0 = 3.5) (c) Using the secant method (three iterations, x-1 = 2.5 and x0 = 3.5) (d) Determine all roots with MATLAB 5. Write an M-file to perform sequential synthetic division and polynomial deflation of the following fourth-order polynomial: f(x) = x4 – 4x3 – 7x2 + 22x + 24 Use the following roots in the following order: (x – 4), (x – 3), (x + 2), and (x + 1)
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Explanation & Answer

Attached.

1

ENGR 328 Homework 4
Question 1:

Answer :
Matlab Code:

Output:

2

Question 2:

Answer:
a. Graphically:
Matlab code:
%(a) graphically
x = -10:.01:10;
f = @(x) log(x...


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