Architecture Commons^™

การติดตามผลการนำแอปพลิเคชันไปใช้ในการจัดการนิติบุคคลในอาคารชุดพักอาศัย, อริยา อริยโชติมา

Chulalongkorn University Theses and Dissertations (Chula ETD)

จากจำนวนโครงการที่อยู่อาศัยที่เพิ่มขึ้น โดยเฉพาะอาคารชุดพักอาศัยในกรุงเทพมหานครและปริมณฑล ส่งผลให้บริษัทบริหารนิติบุคคลมีบทบาทสำคัญมากขึ้น และเกิดการแข่งขันในด้านการบริหารจัดการนิติบุคคลอย่างเข้มข้น หนึ่งในกลยุทธ์ที่บริษัทเหล่านี้นำมาใช้คือการนำเทคโนโลยีเข้ามาช่วยเพิ่มประสิทธิภาพในการบริหารจัดการนิติบุคคล ซึ่งรวมถึงการพัฒนาแอปพลิเคชันนิติบุคคล งานวิจัยนี้มุ่งศึกษาและติดตามผลการนำแอปพลิเคชันนิติบุคคลมาใช้ในอาคารชุดพักอาศัย โดยมีวัตถุประสงค์ดังนี้ 1. ศึกษากระบวนการดำเนินงานและแนวคิดของบริษัทที่บริหารจัดการนิติบุคคล 2. วิเคราะห์ข้อดีและข้อจำกัดของการใช้งานแอปพลิเคชันและ3. เสนอแนวทางการพัฒนาแอปพลิเคชันเพื่อเพิ่มประสิทธิภาพในการบริหารจัดการและความพึงพอใจของผู้อยู่อาศัย และการวิจัยนี้ใช้วิธีการวิจัยแบบผสมผสาน โดยเก็บข้อมูลผ่านการสัมภาษณ์และแบบสอบถามจากกรณีศึกษา ผลการศึกษาพบว่า การระบาดของโควิด 19 เป็นปัจจัยในการเร่งในการพัฒนาและรูปแบบพัฒนาแอปพลิเคชันนั้นสามารถเลือกพัฒนาได้ทั้งแบบการจัดจ้างบริษัทภายนอกหรือทีมภายในองค์กร ตามทรัพยากรที่มีทั้ง งบประมาณ บุคลากร เวลา และความรู้ โดยตัวแอปพลิเคชันนั้นประกอบไปด้วยระบบหน้าบ้านที่เป็นส่วนที่ลูกบ้านเห็นและให้บริการลูกบ้านและระบบหลังบ้านซึ่งใช้ในการทำงานของนิติบุคคล ซึ่งมุมมองของนิติบุคคลในการใช้แอปพลิเคชันพบว่า ช่วยเพิ่มความโปร่งใสในการจัดการงานนิติบุคคลในโครงการ รวมถึงจัดการระบบและข้อมูลได้อย่างเป็นระเบียบ อย่างไรก็ตามพบข้อจำกัดในด้านต่าง ๆ ได้แก่ ความไม่เสถียรของระบบ ความยากในการใช้งานแอปพลิเคชัน และการไม่รองรับการใช้งานของอุปกรณ์บางประเภท และในมุมมองของลูกบ้านแอปพลิเคชันช่วยเพิ่มความสะดวกและความรวดเร็วในการติดต่อสื่อสาร ให้บริการ 24 ชั่วโมง โดยฟีเจอร์ที่ใช้บ่อย ได้แก่ การชำระค่าส่วนกลาง การแจ้งซ่อม และการรับพัสดุ และผลความพึงพอใจด้านคุณภาพแอปพลิเคชันและความพึงพอใจของคุณภาพบริการของโครงการ TLP มีระดับคะแนนค่าเฉลี่ยที่มากกว่าโครงการ KKS แสดงให้เห็นถึงความสำคัญของแอปพลิเคชันของโครงการ TLP ที่มากกว่า KKS ซึ่งสะท้อนในเรื่องของผลพฤติกรรมการใช้งานและแนวคิดในการออกแบบเช่นกัน ทั้งนี้งานวิจัยนี้เสนอแนวทางสำหรับผู้พัฒนาแอปพลิเคชัน ควรให้ความสำคัญกับการออกแบบที่ใช้งานง่าย การเพิ่มความเสถียรของระบบ ความถูกต้องของข้อมูล และการพัฒนาฟีเจอร์ที่ตอบโจทย์การใช้งานจริงเพื่อให้การใช้งานแอปพลิเคชันตอบสนองต่อความต้องการของผู้ใช้งานได้อย่างมีประสิทธิภาพ

Architectural Design Criteria For Achieving Feng Shui Balance For Chinese Immigrant Houses In Chonburi, Thailand, Yu Peng Huang

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis examines how Form School Feng Shui principles can guide residential design for Chinese migrant workers in Chonburi, Thailand. The study addresses the problem of cultural and environmental incongruence in local townhouse layouts, particularly in the arrangement of Yin and Yang spaces and natural ventilation, which are essential to creating a balanced living environment in Feng Shui. The work is significant as it adapts Feng Shui architecture—a system deeply rooted in Chinese philosophy—to a modern context, fostering cultural familiarity and comfort for migrants. Using a comparative analysis of traditional Chaoshan courtyard houses and townhouses in Chonburi, the research evaluates …

Prosthetic Architecture: Lingering For Nostalgic Futurism, Sahasrungsri Wajchathon

Chulalongkorn University Theses and Dissertations (Chula ETD)

This thesis explores prosthetic architecture, a concept that combines nostalgia and futurism to reimagine the conservation of architecture in everyday life. Inspired by the idea of architecture as a "prosthesis" that extends and adapts to modern needs, the objective is to propose an alternative approach to architectural conservation — one that not only preserves cultural and historical value but also integrates new infrastructure and functions to align with contemporary lifestyles. By reviewing key theories, such as Sigmund Freud's views in Civilization and its Discontents and Mark Wigley's Prosthetic Theory: The Disciplining of Architecture, this research builds a theoretical foundation for …

Aging In Place With A Warming Climate: Housing Design And Policies For Aging With Extreme Heat, Nichole M. Kain

Antioch University Dissertations & Theses

Aging populations—particularly in areas prone to extreme heat—are facing unique residential challenges. In the past 10 years, extreme heat has killed more people in the United States (U.S.) than all other weather hazards combined, and it is expected to get hotter, with extreme heat events predicted to happen more often in the future. People over the age of 65 are disproportionately represented as the majority of heat victims, and are likely to perish in their own homes during these events. Every day, 10,000 people turn age 65 in the U.S. and many are choosing to age and retire in places …

Quantifying The Role Of Insurance In Tornado-Impacted Community Recovery: A Survey And Simulation-Based Approach, Jie Zhao, Ji Yun Lee, Guirong Grace Yan, Fangjiao Ma

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Insurance against disasters plays a critical role in community recovery by providing policyholders with reliable and timely payments for repairing or reconstructing damaged houses. By allowing homeowners to transfer risk, insurance enables homeowners to address house without experiencing significant financial burdens. Although historical events have highlighted the importance of insurance, its quantitative impact on community recovery, particularly in tornado-impacted communities, is understudied. This study focuses on advancing our understanding of whether sufficiently insured houses can have a positive impact on the recovery of tornado-impacted communities (i.e., the main research question). This paper proposes a two-stage simulation framework to quantitatively evaluate …

Prediction Of Carbonation Capacity Of Scms Using Ensemble Learning Method, Kangyi Cai, Jian Liu, Edward Mwanza, Mahelet G. Fikru, Hongyan Ma, Donald C. Wunsch

Economics Faculty Research & Creative Works

The utilization of supplementary cementitious materials (SCMs) subjected to carbonation processing represents a viable strategy to mitigate anthropogenic CO₂ emissions associated with concrete production, potentially contributing to the achievement of carbon neutrality. However, existing studies have limitations in effectively predicting the varying carbonation capacities of different SCMs, a gap that this research aims to address. Recent research efforts focused on the carbonation of waste-material-sourced SCMs are reviewed, along with a comparative discussion on diverse carbonation methods. A detailed data set encapsulating the properties of SCMs, and carbonation configurations was compiled. At the same time, six ensemble learning models were …

Beneficiation Of Lunar Regolith Simulants Through Electrostatic Sieving And Magnetic Separation, Peter Bachle, Jeffrey Smith, Fateme Rezaei, David Bayless, William Schonberg, Daoru Han

Materials Science and Engineering Faculty Research & Creative Works

In the light of future development of lunar structures, in-situ feldspar beneficiation is imperative for metal extraction. This research incorporates the tandem use of electrostatic sieving and magnetic separation for collecting a specific size range and mineral composition from lunar soil that optimizes subsequent chemical processing. While earlier works focused on silt-sized particles, this work expands that range up to medium-grained sand with a greater variety of potential lunar regolith compositions. This work shows that a 2.5 kV, 7 Hz to 30Hz frequency, single-phase square wave can lift silt and fine sand for collection. This lifting is successful directly from …

Kinetic Modeling Of Electrostatic Sieving For Lunar Regolith Beneficiation: Case Studies, Easton Ingram, Emmanuela Amen Eze, Jeffrey Smith, Fateme Rezaei, David Bayless, William Schonberg, Daoru Han

Materials Science and Engineering Faculty Research & Creative Works

A new kinetic particle modeling framework was developed to investigate electrostatic transport of lunar regolith particles with applications to the concept of electrostatic sieving. The new approach is based on kinetic particle dynamics and includes major modules of sampling the particle size distribution, solving electric fields, and tracking motion of charged dust grains. Case studies for a concept of electrostatic sieving were chosen to validate the new model. The simulation achieved similar yields reported in previous works, which served as validation of the model. The new model is computationally efficient and could serve as a design, analysis, and optimization tool.

Photogrammetry-Based Method For Measuring Volume Changes Of Soil Specimens During Critical Phases Of Triaxial Testing, Sara Fayek, Xiong Zhang, Pingxin Xia

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Triaxial tests has been routinely used to measure the stress–strain relationship for geomaterials. During triaxial testing, many sources of errors that cannot be completely avoided but are often ignored or approximated using empirical equations. This paper presents a systematic investigation of soil volume change, volume strain nonuniformity, and cross-sectional calculation along the specimen during triaxial testing using a photogrammetry-based method. Consolidated drained triaxial tests were performed in which two parallel measurements were taken: (1) relative volume using the conventional triaxial testing and (2) absolute volume using the photogrammetry-based method. The difference in the observed volume and void ratio measurements between …

Effect Of Concrete Mix Design Factors On Static Yield Stress Changes Due To Vibration, Ahmed Abd El Fattah, Dimitri Feys, Kyle Riding, Syed Imran

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Digital fabrication of concrete structures has gained substantial research traction over the last decade, enabling efficient material use and adding more architectural freedom. Current research focuses on chemical and mineral admixtures, as well as manipulating the cement hydration reaction to control the yield stress evolution with time in the cement paste. Instead of providing yield stress through the concrete fluid properties, a high yield stress can be provided by interparticle friction from the use of high aggregate volumes and large nominal maximum aggregate size, with flow enhanced for material extrusion by vibration. Granular physics was applied to concrete mixture design …

Biobased Construction From Agricultural Crops: Paper 2 - Supply Chain Dynamics Of European Case Studies, Patrick Daly, Paula G. Barril

Articles

Energy security, economics and environmental factors are key drivers toward greater energy efficiency, decarbonisation and circularisation of the building sector.

Bio-based construction provides a potential low carbon and circular strategy toward these aims, as these materials can sequester carbon, are derived from renewable and nontoxic sources and can be re circulated in either technical or bio cycles.

This innovative research undertakes a state of play into select agri-crop biobased construction materials, products and systems across Europe focusing on their supply chain types and dynamics.

The research is based on a multi case study applying a range of mainly qualitative research …

The Hydration, Microstructure, And Mechanical Properties Of Vaterite Calcined Clay Cement (Vc³), Yaqiang Li, Yue Li, Hongyan Ma, Jiaqi Li

Civil, Architectural and Environmental Engineering Faculty Research & Creative Works

Limestone (calcite) calcined clay cement (LC3) is a promising low-CO2 binder, but the low activity of calcite cannot compensate the reduction in clinker factor, resulting in low one-day strength and limiting its broad applications. As recent carbon capture and utilization technologies allow scalable production of vaterite, a more reactive CaCO3 polymorph, we overcome the challenge by introducing vaterite calcined clay cement (VC3), inspired by the vaterite-calcite phase change. In the present study, VC3 exhibits higher compressive strengths and faster hydration than LC3. Compared to hydrated LC3, hydrated VC3 exhibits increased amount of hemi- and mono-carboaluminate formation and decreased amount of …

A Concept Of Producing Aluminum In-Situ On The Moon Through Molten Salt Electrolysis, Jacob N. Ortega, Jeffrey Smith, Fateme Rezaei, David Bayless, William Schonberg, Daniel Stutts, Daoru Han

Materials Science and Engineering Faculty Research & Creative Works

This paper presents a concept of producing aluminum in-situ on the lunar surface, namely, the Lunar In-Situ Aluminum Production through Molten Salt Electrolysis (LISAP-MSE) method developed at Missouri University of Science and Technology. This paper aims to demonstrate the use of electro-deoxidation to reduce aluminum oxide (i.e., alumina) into aluminum and oxygen gas via electrolysis in a molten salt bath for the production of aluminum on the Moon. It is shown that with a steady supply of hydrogen chloride, this in-situ resource utilization (ISRU) method could supply several necessary materials consumed in the electro-deoxidation process except hydrogen chloride to produce …

To What Extent Does Lighting Affect Students’ Preference For Seating In The Georgia Southern University Henderson Library?, Hailey M. Hawkins

Honors College Theses

This study highlights the importance of lighting in academic library spaces, specifically in relation to students' seating choices and overall experience. The research is significant as it emphasizes the role that environmental factors can play in creating a conducive learning environment for students. The study utilized a mixed-methods approach, which combines quantitative and qualitative data collection methods to provide a comprehensive understanding of students' lighting preferences. The quantitative data collected through open observations and the use of a light meter provided insights into the relationship between lighting and seating choices. The qualitative data collected through questionnaires helped to understand the …

The Effect Of Lighting In Higher Education Classrooms On College Students, Caitlin M. Nelms

Honors College Theses

Classroom lighting design is important for student learning outcomes, and can have a negative effect on the physiological states of students. Interior lighting design needs to include appropriate layers of artificial and daylighting. Previous models have shown that artificial lighting can be altered to give off the same effect of natural daylight. Studies have also shown that natural lighting has a positive effect on the productivity of students in a classroom environment. Data was collected by surveying students in a classroom with no natural lighting to see how they felt in the room and if they have any lighting recommendations …

Melissa Brown Collection Of "A Loud Absence" Project Materials, Zach S. Henderson Library, Special Collections

Finding Aids

This collection consists of photographs and digital files created by artist Melissa Brown as part of her project, titled "A Loud Absence." According to the artist, the project sought to discover what happens to a space after great injustice has been committed in it. The project examines whether a community's choice of what to do with such an area reflects healing or reveals that they have not moved forward from their past.

The Future Of Building: The Potential Impacts Of 3d Printing Within The Construction Industry, Alyssa Morrison

Honors Theses and Capstones

This research investigates the expanding practice of 3D printing in construction, focusing on its potential impacts and challenges it will face within the industry. Emphasizing both its sustainability and cost-saving benefits, this paper examines how 3D printing could potentially revolutionize traditional building methods. The ability to decrease greenhouse gas emissions, address the global housing shortage, and reduce material waste are addressed. Through interviews with industry professionals, as well as a thorough literature review, the research explores the factors driving interest and investment in 3D printing technology. Additionally, it analyzes common misconceptions regarding 3D printed structures and pinpoints areas for further …

Influence Of Macro-Synthetic Fibers On The Flexural Behavior Of High Strength Concrete Beams Reinforced With Gfrp Bars, Maryam M. Koura, Ahmed M. Tahwia, Mohamed H. Matthana

Mansoura Engineering Journal

Rusting of steel reinforcement in marine environments causes the overall destruction of reinforced concrete constructions; steel rebars in concrete members have been replaced with fiber-reinforced polymer (FRP) bars in recent years. To enhance the shear behavior of glass (GFRP) bars reinforced concrete (RC), macro-synthetic polyolefin (PO) fiber was added. These materials have a low modulus of elasticity, a high tensile strength, and a linear stress-strain response to full failure. This study investigates the effect of macro synthetic structural fibers on the post-cracking and deformability properties of high strength concrete reinforced with FRP bars without transverse reinforcement. Eight full-scale RC beams …

Unleashing The Potential: The Impact Of Biophilic Office Design On Enhancing Employee Productivity, Asmaa Elantary

Mansoura Engineering Journal

The observed landscape influences people in numerous ways, including aesthetic appreciation, health, and well-being. The evidence of health benefits associated with viewing those landscapes has proven exceptional value. A comprehensive review of papers on landscapes and sound effects on health was conducted. According to a growing body of evidence, exposure to visible landscapes positively affects one's health and fitness. The most pressing social and economic challenge now is increasing worker productivity, attracting, and retaining exceptionally talented employees, and improving overall employee performance. This will not happen unless companies provide a safe, comfortable, and stimulating work environment; this will not happen. …

Maximum/Minimum Output Current Extraction Based Open-Switch Fault Diagnosis Of Voltage Source Inverter, Ahmed S. Gardouh, Eid Gouda, Abdelhady Ghanem

Mansoura Engineering Journal

Three-phase induction motor drive systems face significant susceptibility to critical failures arising from open switch faults within the power electronic converter. Implementing monitoring and early fault detection mechanisms for such occurrences not only enhances system reliability but also ensures the safe and uninterrupted operation of the motor drive system. This study introduces an innovative real-time open switch fault detection technique for voltage source inverters fed induction motor drives, leveraging motor stator current analysis. The method aims to track maximum and minimum values of current signals over one cycle. Unlike many current signal-based approaches that require modifications to be integrated with …

Pathways To Health: Linking Accessible Green Space To Improved Health And Well‐Being In Rural Appalachia., Udday Shankur Datta

Graduate Theses, Dissertations, and Problem Reports (ETD)

Green spaces are essential for our physical health. The quality of its green space often determines the health of a community. The presence of green space in our lives is associated with reduced stress levels, better sleep, and increased feelings of safety. Lack of access to green space can lead to many health issues, such as high blood pressure, diabetes, and cardiovascular diseases, and has been linked to obesity and physical inactivity.

The Appalachian Regional Commission (ARC) defines Appalachia as a region covering 420 counties across 13 states in the eastern United States. A large part of this region is …

Ecological Planning And Design For Creating A Thriving Suburban Community In Lumberton, Nc, Maram Moushmoush

Graduate Theses, Dissertations, and Problem Reports (ETD)

The purpose of the project is to propose ecological planning and design techniques to create a thriving and robust suburban community in Lumberton, North Carolina. The project becomes an educational hub on agroforestry, ecological design and stewardship, and flood mitigation through stormwater strategies for Linkhaw’s Mixed Use Community Development plan. Linkhaw Farms is a 540 acre site, in a predominantly Native American community, situated on the north-east boundary of Lumberton in the Coastal Plains region of NC. It was formerly owned by the Linkhaw family for over 70 years, producing tobacco, and later rotation of annual crop production between corn …

Acknowledgment Note

Mansoura Engineering Journal

No Abstract

Production Of Hydrogen From Sodium Borohydride Using Bimetal Catalyst, Haitham I. Attia, Hani Mahanna, M.M. El-Halwany, Mahmoud H Mahmoud

Mansoura Engineering Journal

Here, in this paper we try to focus on the bi-metal non-semiconductor photo catalyst for the Production of hydrogen from sodium borohydride instead of semi conductor photo catalyst which have an excellent performance in photo-catalysis. In this paper , we studied the combination of CuNi bi-metal(developed and reinforced on MWCNTs) as a non-semiconductor photo-catalyst that generates electrons for the Production of hydrogen from sodium borohydride with led light as source of light , We also added CuNi on multi wall carbon nano tubes (MWCNTs) for increasing the surface area of the reaction. We studied the effect of different quantity of …

The Dynamic Stability Of The Sewing Needle’S Mechanical Vibrations Under The Impact Of A Time-Dependent Penetration Force In The Multilayered Sewn Fabrics, Wael A. Hashima, Ibrahim A. Elhawary

Mansoura Engineering Journal

In this work the dynamic stability of the mechanical vibrations of the sewing needle during sewing process under the impact of the time dependent penetration force (cyclic type) were studied. The many mathematical equations were written and explained for both of the sewing needle dynamics and penetration force mechanics. They were related to the regions of sewing needle stability regions either mathematically or graphically. Mate equation (difficult one) was refereed to help in investigation the sewing dynamic stability during sewing process.

A 10-Gb/S Single-Loop Half-Rate Dll-Based Clock And Data Recovery Circuit For Forwarded-Clock Wireline Transceivers, Abdallah K. Mohamed, Sameh A. Ibrahim, Mohy Eldin A. Abo-Elsoud

Mansoura Engineering Journal

This paper introduces a 10-Gb/s single-loop, half-rate delay-locked loop (DLL)-based clock and data recovery (CDR) circuit for forwarded-clock (FC) wireline transceivers. The proposed CDR employs a differential ring oscillator (RO) with sub-feedback loops structure for multi-phase clock generation with a single-loop operation. An Alexander phase detector utilizing a flip-flop based on an improved true single-phase clock (TSPC) logic with split outputs is adopted. The proposed DLL-based CDR is an optimized solution in terms of area and power for FC wireline transceivers. The recovered clock exhibits an RMS jitter of 590 fs and a peak-to-peak jitter of 3.8 ps. The circuit …

Laboratory Characteristics, Performance Evaluation, And Agency Cost Analysis Of Cold-Recycled Asphalt Mixtures, Marwa B. Elaskary, Ahmed M. Awed, Alaa R. Gabr, Sherif M. El-Badawy

Mansoura Engineering Journal

This technical study offers a comprehensive investigation into the utilization of Cold Recycled Asphalt Mixtures (CRAMs) with varying proportions of Reclaimed Asphalt Pavement (RAP) in the context of pavement maintenance applications. The study encompasses a multi-faceted analysis, encompassing laboratory mix design requirements, mix performance evaluations, and a thorough assessment of economic benefits, with the overarching goal of promoting the sustainable adoption of CRAMs in pavement maintenance. To achieve the objectives of the research, five ratios of RAP to virgin aggregates (VA) of (0%:100%), (25%:75%), (50%:50%), (75%:25%), and (100%: 0%). The research encompasses a wide array of laboratory tests and investigations …

Enhancing The Garment Quality Through The Integration Of Statistical Techniques, Magdi El Messiry, Affaf Al-Oufy, Heba Marwan, Samar Abd-Ellatif

Mansoura Engineering Journal

The textile and apparel sector has always held significant strategic value for the economies of numerous developing countries. These industries represent vital components of manufacturing and exports, playing a major role in employment opportunities. Within the realm of garment production, a strong emphasis on quality is maintained throughout the entire process, starting from sourcing raw materials and extending to the final stages of garment completion.

This research undertaking involves a comprehensive analysis, classification, and evaluation of defects in fabrics and garments. Frequencies and distributions of these defects are being looked after with great caution. To enhance product quality, the application …

Application Of Machine Learning Models In The Capacity Prediction Of Ccfst Columns, Khaled Megahed, Nabil Said Mahmoud, Saad Elden Mostafa Abd-Rabou

Mansoura Engineering Journal

Circular concrete-filled steel tubular (CCFST) columns are widely utilized in structural engineering due to their impressive load-bearing capabilities and ductility. Existing design standards often yield disparate outcomes when applied to structural columns with identical properties, introducing uncertainty for engineering designers. This study introduces an innovative technique to address these challenges using two machine learning (ML) models: Gaussian process regression (GPR) and extreme gradient boosting (XGBoost). These models consider various input variables, including the geometric and material properties of CCFST columns, to estimate the compressive strength. The models undergo training and evaluation using two datasets comprising 1004 axially loaded CCFST columns …

Numerical And Analytical Solution For Nonlinear Free Vibration Of Tapered Beams, Zain Abu Shaeer Abu Shaeer, Ramy I. Shahin, Galal I. El-Baghdady, Saad A. Yehia

Mansoura Engineering Journal

This study introduces a computational approach that combines numerical and semi-analytical methods to solve tapered beams' nonlinear free vibration equation. The study employs a numerical approach that relies on the cubic B-spline collocation method and an approximation technique known as the Homotopy perturbation method to approximate the solution to the equation governing nonlinear large-amplitude free vibrations of tapered beams. The effect of vibration amplitude on the frequency of nonlinear vibrations is investigated. The next step is to look at different ways to get close to exact solutions across the whole range of oscillation amplitude. This will show how useful and …