parts 1,2,3,4 please You are working as an Engineering Technician at GEMR, which specializes in designing and developingmedical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and RadioFrequency (RF) antennas coils. You will be working with the MRI and RF coils team to design a threeantenna RF coil, as shown in Figure 1(b), to be used in conjunction with an MR machine. The RF coil willbe placed on the patient head during the MR scan, see Figure 1(a). The RF coil will be exposed to an RFpulse that is in conjunction with the magnetic field of the MR scanner, Figure 1(a), receives signals fromthe brain as current flowing in the antennas. These currents are then converted into an image of thebrain as seen in Figure 1(c). Your responsibility is to carry out mathematical analysis of the RF coil topredict the performance of the antennas before they can be tested on human beings.RF PuleAntenna Aetenna 2 Aatensa 3(a)Figare 1: (a) MR machine, (b) throe loop antenmax, and (0) brain MR image Analysis 2:The voltage potential, v(t), builds up on the loops, based on the orientation of the magnetic field duringan MR scan is given by:v[t) = 0.250t4 + 0.166t3 – 0.500t2And 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 theinterval [-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 theintervals [0.3:0.7] and [-1:-5]. Calculate the percentage of error. Show details of your steps.

Name: parts 1,2,3,4 please You are working as an Engineering Technician at G
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Description: parts 1,2,3,4 please You are working as an Engineering Technician at GEMR, which specializes in designing and developingmedical equipment such as Magnetic Resonance Imaging (MRI) systems, X-ray systems, and RadioFrequency (RF) antennas coils. You wil

1) Given that, the voltage potential function is vt=0.250t4+0.166t3-0.500t2. Differentiate the…

Math

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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 – 0.500t2 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 timetE [-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 – 0.500t2 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 timetE [-4 : 4]. 3. Find the roots of vr(t) analytically.

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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parts 1,2,3,4 please

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

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.

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