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Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t4 + 0.166t3 – 0.500 and the voltage at time t= 0 is 0. Al Hussein Technical University 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 :4]. 3. Find the roots of vr(t) analytically.

Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t4 + 0.166t3 – 0.500 and the voltage at time t= 0 is 0. Al Hussein Technical University 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 :4]. 3. Find the roots of vr(t) analytically.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t4 + 0.166t3 – 0.500? and the voltage at time t = 0 is 0. Al Hussein Technical University 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 :4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in the interval [-4 : 4]? If yes, estimate the roots graphically. 5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps. 6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps. You should validate the mathematical model for your solutions using MATLAB. Show details of your program and results. You should compare between the Bisection and the Newton-Raphson methods applied in terms of applicability, accuracy, and converging speed.
Transcribed Image Text:Analysis 2: The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field during an MR scan is given by: v(t) = 0.250t4 + 0.166t3 – 0.500? and the voltage at time t = 0 is 0. Al Hussein Technical University 1. Formulate the mathematical model for the voltage rate vr(t) developed at the loops during scanning. 2. Plot/Sketch vr(t) as a function of time t E [-4 :4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vr(t) in the time interval [-4 : 4]. Does vr(t) have any root in the interval [-4 : 4]? If yes, estimate the roots graphically. 5. Manually use Bisection iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps. 6. Manually use Newton-Raphson iterative technique with 6 iterations to find a root of vr(t) in the intervals [0.3 : 0.7] and [-1 : -5]. Calculate the percentage of error. Show details of your steps. You should validate the mathematical model for your solutions using MATLAB. Show details of your program and results. You should compare between the Bisection and the Newton-Raphson methods applied in terms of applicability, accuracy, and converging speed.
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