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.
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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Question
Answer the question part (4,5,6)
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd33a302c-5a87-4ac3-9fd5-588f60b73fc9%2F10389621-3968-40de-a302-98ef5b6769a6%2Fm4eaurs_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 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:Derivative of a function finwith respect to ris the measure of how fast the function is changing
r()
with respect to L Mathematically the derivative at a point is defined asf
= lim
MM>0, the function is increasing with respect to, similarly if/()<Othe functionis
decreasing with respect to r
According to the standard results, the derivative of the is =n,where i is an integer.
If a is a constant, then derivative of function in the form af() is (af ()) = af (1).
The equation for magnetic field that developed under the presence of magnetic field is given
by v(r) = 0. 250r+0, 166r – 0. 500r. To find a mathematical model for the voltage rate,
differentiate the function vr) with respect to time, Use the result = nrto simplify the
expression.
vr)%3D(0.25o +0.166-0.500)
= 4+0. 1664-0.5004
0.250
-0.250-4 + 0,166 - 3r- 0.500-2r
=1.000 +0.4987-1.000
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