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part 6 please

part 6 please

Advanced Engineering Mathematics
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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part 6 please

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 – 0.500t2 And the voltage at time t = 0 is 0. 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€ [-4:4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vrlt) in the time interval [-4 : 4]. Does yrdt) 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 yr(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 yr(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 – 0.500t2 And the voltage at time t = 0 is 0. 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€ [-4:4]. 3. Find the roots of vr(t) analytically. 4. Use your figure to study the sign of vrlt) in the time interval [-4 : 4]. Does yrdt) 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 yr(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 yr(t) in the intervals [0.3:0.7] and [-1:-5]. Calculate the percentage of error. Show details of your steps.
You are working as an Engineering Technician at GEMR, which specializes in designing and developing medical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and Radio Frequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a three antenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil will be placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RF pulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals from the brain as current flowing in the antennas. These currents are then converted into an image of the brain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil to predict the performance of the antennas before they can be tested on human beings. RF Pule Antenna Aetenna 2 Aatensa 3 (a) Figare 1: (a) MR machine, (b) throe loop antenmax, and (0) brain MR image
Transcribed Image Text:You are working as an Engineering Technician at GEMR, which specializes in designing and developing medical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and Radio Frequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a three antenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil will be placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RF pulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals from the brain as current flowing in the antennas. These currents are then converted into an image of the brain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil to predict the performance of the antennas before they can be tested on human beings. RF Pule Antenna Aetenna 2 Aatensa 3 (a) Figare 1: (a) MR machine, (b) throe loop antenmax, and (0) brain MR image
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