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 – 0.5002 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.
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 – 0.5002 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve 2&3&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) = 0.250t4 + 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 compare between the Bisection and the Newton-Raphson methods applied in terms of
applicability, accuracy, and converging speed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe307a8c5-c2c8-49b8-86cf-86f8f56d3fb5%2Fd9aed89f-80cb-465c-8162-872f1c835280%2F99ad7z_processed.jpeg&w=3840&q=75)
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 compare between the Bisection and the Newton-Raphson methods applied in terms of
applicability, accuracy, and converging speed.
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