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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) = 0.250t* + 0.166t³ – 0.500r and the voltage at time t=0 is 0. Al Hussein iccnica 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].

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) = 0.250t* + 0.166t³ – 0.500r and the voltage at time t=0 is 0. Al Hussein iccnica 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].

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter3: Additional Topics In Trigonometry
Section3.3: Vectors In The Plane
Problem 84E
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compare between the Bisection and the Newton-Raphson methods applied in terms of applicability, accuracy, and converging speed.

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 icchnical 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.
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 icchnical 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.
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