Saturday, January 25, 2020

Example Physics Essay

Example Physics Essay The Motion of a Mass Spring System The example of a mass attached to the end of a spring is a powerful tool in physics due to the fact that it is analogous to many physical phenomena. To be able to use this example to elegantly describe other more complex systems it is crucial to first fully understand how this simple system works itself. The force acting on a mass attached to a spring at a given position is given by (Serway, 2003: 437). F= -kx (Eqn 1) This equation may be derived from Newton’s Second Law of motion, which states that the force on a mass is proportional to the rate of change in momentum. A mass and spring system can be described as a Simple Harmonic Oscillator and there are some fundamental equations that govern the motion of such a system (Serway, 2003: 436). ω= √(k/m) (Eqn 2) Equation two shows how the angular frequency (ω=2Ï€*frequency) of an object oscillating due to it being fixed to a spring that is inversely proportional to the mass of the object. k is a constant, known as the spring constant that is defined by the properties of the spring. k can be easily determined experimentally for a given spring by changing the mass attached to the spring and measuring the frequency. Due to the periodic nature of such a system as that which can be described using equations one and two, they are known to be in simple harmonic motion. The motion of a particle over time is described effectively by a cosine wave (Serway, 2003: 436; Hayek , 2003; 562). x(t)=Acos(ωt+à Ã¢â‚¬ ¢) (Eqn 3) Equation three shows how this motion can be mapped over time where A is the amplitude of the oscillation, and à Ã¢â‚¬ ¢ is a term to correct the phase. This can be plotted to show how the mass and spring system will move over time. The figure above shows how a mass on a spring will behave in a frictionless universe while obeying Newton’s First Law of motion. A useful trait of the Simple Harmonic Oscillator is that the equations for the velocity and the acceleration are easily derived from that of the position equation (Serway, 2003: 436). V(t)=-Aω.sinà ¢Ã‚ Ã‚ ¡(ωt) (Eqn 4) a(t)= -Aω ² cosà ¢Ã‚ Ã‚ ¡(ωt) (Eqn 5) For brevity the phase term (à Ã¢â‚¬ ¢) has been omitted from these two equations as it can be assumed that phase is the same. These two equations give valuable insight into the nature of as mass on a spring and how its velocity and acceleration is linked. The interesting thing to note is that velocity is governed by a sine waveform, yet acceleration is dependent on the cosine waveform. What this means is that when the particle on the spring has minimum velocity it will have maximum acceleration, it also means that when the mass is travelling at its maximum velocity it has minimum (possibly zero) acceleration. Realistically however, most situations where a simple harmonic oscillator may be applied will involve a resistive force of some description, such as friction in the case of a mass on a spring. The effect this has on the motion of the mass and the spring system can be seen in the figure below. It is clear to see on the above figure that the presence of friction causes the amplitude of the oscillation to decay over time. This effect is known as damping. In a damped system that has no external force driving the oscillation itself, the rate at which the oscillation decreases is directly proportional to the resistive force being applied to it. The damping force is at its greatest when the particle is moving at its fastest velocity and at a minimum when the acceleration is at a maximum. There are three types of damping in an oscillatory system, underdamping, over-damping and critically damped. Underdamped is where the amplitude of the decay envelope does not decay rapidly. Critically damped systems are the fastest to return to equilibrium and will have a decay envelope that allows one oscillation over the entire damping period and will decay towards zero rapidly during this period. Over-damping occurs when there are no oscillations (as seen in critical damping) however there is an infinite time to return to equilibrium (Hayek , 2003; 567). The equation which describes this damped oscillation is given by: F= -kx-l dx/dt (Eqn 6) Here the original equation for the force is extended by a first order differential term relating to the change in the velocity due to the damping constant l. Equation six is able to be expanded into a more useful form by applying Newton’s Second Law, which gives: (d ² x)/(dt ² )+2Dω_0 dx/dt+ω_0 ² x=0 (Eqn 7) This equation now contains a first and second order differential equation relating to the velocity and acceleration respectively of the particle. Equation seven looks to be much more complex than that of equation six, however it is now in a considerably more useful form as it allows to see equation six in terms of the angular frequency of the system. D is the damping ratio and is given by D= l/(2√mk) , taking into account the damping coefficient, the spring constant and the mass of the particle. To fully understand the motion of the mass and spring system there must be consideration of the energy within the system. This may be done with the help of some simple drawings. The blue lines indicate the spring and the solid red block with a blue border indicates the mass. From the figures it is possible to imagine stretching the spring, this means that there is a force acting on the mass and if it is held at this stretched point (x) the mass will have a potential energy U. should the mass be released from this point it will have a maximum velocity Vmax and a maximum Kinetic energy KEmax. The total energy in the system at any one point in time is the sum of the potential and kinetic energies. E(t)=KE+U (Eqn 8) E(t)=1/2 mà £Ã¢â€š ¬Ã¢â‚¬â€œv(t)à £Ã¢â€š ¬Ã¢â‚¬â€Ã‚ ²+1/2 kà £Ã¢â€š ¬Ã¢â‚¬â€œx(t)à £Ã¢â€š ¬Ã¢â‚¬â€Ã‚ ² (Eqn 9) By substituting the formulae for velocity and position (equations three and four) into the energy equation it is possible to simplify this further. E(t)= 1/2 kA ² [à £Ã¢â€š ¬Ã¢â‚¬â€œsinà ¢Ã‚ Ã‚ ¡(ωt)à £Ã¢â€š ¬Ã¢â‚¬â€Ã‚ ²+à £Ã¢â€š ¬Ã¢â‚¬â€œcosà ¢Ã‚ Ã‚ ¡(ωt)à £Ã¢â€š ¬Ã¢â‚¬â€Ã‚ ² ] (Eqn 10) E(t)=1/2 kA ² (Eqn 11) The elegance of this simple algebra is that for an oscillating mass on a spring the energy in the system at any given point in time is completely independent of time. If there are dissipative or driving affects occurring during the oscillations then the amount of energy in the system will change, however for a closed system this fact holds true. This equation occurs in many areas of physics, for much more complex systems than a single mass on a spring. These equations can be applied to pendulums, resonant electrical circuits (RLC circuits) (Mispelter, 2006: 35) such as those used to detect Radio and TV signals, or even in quantum mechanics and the time independent Schrodinger equation, where it is found that a quantum harmonic oscillator, such as a particle in a potential well (Schrà ¶dinger, 1926: 1054), is one of the few quantum mechanical problems that it is possible to find analytical answers for. If the Hamiltonian for such a system is examined it is shown that its structure is very similar to that of equation nine (Schrà ¶dinger, 1926: 1057; Levitt, 2012: 144). H ÃÅ'‚= p ÃÅ'‚/2m+1/2 mω ² x ÃÅ'‚ ² (Eqn 12) p ÃÅ'‚ is the momentum operator that forms the kinetic half of the Hamiltonian and x ÃÅ'‚ is the position operator which calculates the potential part of the Hamiltonian (Schrà ¶dinger, 1926: 1052). It is obvious that the simple classical physics still applies to this quantum system. These are some of the situations where this type of motion is observed and the table shows how the equations are manipulated to fit the system under examination ( Hayek , 2003; 562; Mispelter, 2006: 38; Dirac, 1958: 108; Boylsestad, 2010: 871). In conclusion the mass and spring system’s motion is elegantly described by some simple mathematics that can be manipulated to suit systems that have external forces acting on the motion of the system. The beauty of this is that the mathematics can then be applied to much more complex systems. References: Boylestad, Robert. (2010) Intrductory Circuit Analysis, 12th edition. Pearson. Dirac, P. A. M. (1958). The Principles of Quantum Mechanics, 4th edition. Oxford University Press Hayek, S. I. 2003. Mechanical Vibration and Damping. Encyclopaedia of Applied Physics. Levitt, M. (2012). Spin Dynamics, Basics of Nuclear Magnetic Resonance 2nd edition. John Wiley and Sons Ltd. Mispelter, J. (2006) NMR probeheads for biophysical and biomedical experiments: theoretical principles practical guidelines. Imperial College Press. Schrà ¶dinger, E. (1926). An Undulatory Theory of the Mechanics of Atoms and Molecules. Phys. Rev. 28 (6) pp 1049-1070. Serway, R. A., Jewett, J. W., Serway, R. A. (n.d.). Physics for scientists and engineers, with modern physics. Belmont, CA: Thomson-Brooks/Cole.

Friday, January 17, 2020

Leadership Development Report Essay

Leadership has a paramount importance in the business world. It is not about a position, but how a person can influence others in creating and working towards that common organisation’s goal, and to create meaning in the works that we do. This report begins with the servant leadership framework that covers what I value in leadership. Also included in this report are the self-assessments that measure my leadership potential and competencies. This report also covers the issues associated to the industry I have chosen to work in and address my person-specific issues. II. LEADERSHIP DEVELOPMENT MODEL (175) Definition servant leadership Servant leadership is a type of leadership where the leader does order to be served; but focus on serving their followers in order to assist and guide them into more useful and satisfied people. This theory emphasize on the creation of moral purpose for leaders. It focuses on the impact that they leave on other people’s life to measure their greatness. Characteristics of servant leadership The servant leadership theory consists of ten key characteristics. These characteristics are; listening intently, empathy, healing, awareness, persuasion, conceptualization, foresight, stewardship, commitment to the growth of people, and building community. (Miller, Skringar, Dalglish & Stevens, 2012) Why servant leadership? My concept of leadership is someone who is able to influence their followers through inspiration, empower them to realize their undiscovered true potential, and bring meaning to their life. In addition, I believe that a leader needs to be able to listen to their follower’s need in order to put the will of the group above their own will on the group. I strongly uphold the need for empathy in my leadership concept, because I believe that a leader must be able to put themselves in their follower’s shoes and perceive things through the eyes of their followers in order to gain understanding from different perspectives and to empower the followers to bring out their passion and thus bring forward their fullest potential in making a meaningful work. As mentioned by a successful leader – Fred A. Mansk Jr, â€Å" The ultimate leader is one who is willing to develop people to the point that they eventually surpass him or her in knowledge and ability.† Therefore, I find Servant Leadership as the most suitable framework for my leadership plan. III. Diagnosis of Strength and Weaknesses To support the diagnostic process and to provide the information on my leadership strengths and weaknesses I am using the information from two personality tests; Carl Jung’s and Issabel Briggs Myer’s Typology Test and a standardized emotional intelligent (EI) test. Self Assessments Carl Jung’s and Issabel Briggs Myer’s Typology Test Carl Jung’s and Issabel Briggs Myer’s Typology Test is a psychometric assessment designed to measure the preferences in how people perceive the world and make decisions based on their psychological preference. The aim of this test is to help people to have a better understanding of themselves, by understanding their strengths, weaknesses, possible career preferences and their preferred approach when interacting with others. This test puts one into four letter categories, where each letter stands for a specific personality type. (Briggs, Myers, 1998) After undertaking this typology test, I was classified under INFJ (Introvert, iNtuitive, Feeling, Judging) typology. Firstly, introversion displays a characteristic that is reserved and highly private. This goes in line with my personal characteristic as I look within for meaning and understanding. Secondly, intuition indicates an emphasis on abstract ideas and focusing on the meaning of the bigger picture rather than solid details. Feeling focuses mainly on personal concerns and emotional perception rather than the logical and objective facts. Judging describes about the need to have control by planning, organizing and making decisions as soon as possible because of INFJs’ deep attention on the future. INFJ type is described as having the strengths of being determined and passionate, altruistic, decisive, insightful, creative, inspiring and convincing. Dr. Dranitsaris stated that INFJ leadership style is quiet and influencing. INFJ leaders often lead by inspiring and motivating people with their ideals, working hard to gain the cooperation of others rather than demanding it. In a business context, INFJ leaders also tend to genuinely care about the people and how happy they are with their job. (Dranitsaris, 2009). This describes the traits considered as strengths of the INFJ type: that of being warm, altruistic and passionate. The main motive for every work done is not focused centrally on gaining personal benefit but for the greater good of the broader society; to find value and purpose for every tasks. Also, INFJs are described to be deeply concerned about their relations with people and how it links to humanity. (Heiss, Butt, 1996) These are the strengths I believe I possess in myself and these characteristics go in line with the framework of servant leadership as explained previously. However, the very strong need to have a cause for every work done can serve as a weakness for INFJ. This is because it can become difficult to maintain the drive and energy to complete works when I am not able to derive any deeper purpose or relate the objective of the work to a worthy goal. The complexity INFJ is further seen with the tendency to be idealistic. When objectives are not in line with a meaningful goal, INFJ will incline to grow restless and demotivated overtime. This will affect the effort and end result. The result may deviate from the targeted aim which becomes a conflict with the need for perfection. These weaknesses are worsen with the reserved nature of INFJ which may trigger unexpressed internal conflicts. Emotional Intelligent Test (EI) Emotional Intelligent test, on the other hand is a psychological test which allow an individual to identify their social skills that facilitate their interpersonal behavior. It identifies one’s capacity for goal-oriented adaptive behavior. It focuses on the aspects of intelligence that govern self-knowledge and social adaptation. Below are the results that I have attained from this self-assessment: Strengths Potential Strength Weaknesses – doing well in the area of emotional understanding – chose good forms of resolution for others conflict situations on the test – empathetic – socially insightful – driven towards self-development – healthy approach in resolving conflict situations – doing reasonably well in the area of emotional identification, perception, and expression – act in accordance with your values – lacking in self-motivation – not very assertive – need to strengthen self-esteem – further development needed in personal resilience/hardiness. These strengths indicate that I possess some of the traits that are needed to display the characteristics of a good servant-leader. IV. Industry-Specific Issues Looking into the Hospitality industry, specifically Airlines, I will use Singapore Airlines as a basis of my evaluation. The extent of superior service is paramount for it to establish itself. In order to deliver the standard of service the company has set for itself, it requires highly passionate and motivated employees. One of the elements that contribute to the success of Singapore Airlines is its human resource that highly regards contribution of creative ideas in which rewards are later given. (Singh, 1984) To be passionate, to inspire and to encourage innovation are strengths found in INFJs that match with the traits of Servant Leaders who encourages and motivates the followers to making a meaningful and effective work efforts. V. Person-Specific Issues Gender, age and culture are important aspects to be considered in shaping one’s leadership development. Being someone coming from Asia, the idea of women becoming a leader will face cultural constraints. In the context of organization, becoming a female leader will be more challenging than the male counterpart because there is a strong notion whereby men are born to lead and women to follow or serve and men hold the leadership positions. (Carly, Eagly, 1999). This is still present in the traditional Asian culture. Even to the eyes of the followers, the figure that is seen to be capable of leading goes to male gender. The masculinity possessed becomes a symbol of strength and competency. (Schein, 2001) Instructions led by female leaders are more likely to be followed because of the idea of obedience to authority rather than being influenced through inspiration. The gender-bias corporate culture becomes a huge obstacle in making use of servant-leadership framework as a female. This gender bias is still evident in many office settings of Japanese corporations whereby higher ranking positions are given mostly to male; and in fact Japan seeing a near zero resemblance between women and managers. (Schein, Mueller, 1992) Besides that, age also becomes an issue in determining the level of experience of a professional. Younger age typically indicates limited exposure to the various real-life experiences and this may affect the extent of wisdom in making judgments. VI. Timeframe and Evaluation Plan The weaknesses based on the self-assessments are used to develop my leadership goals and the Michigan Leadership Competency Model serves as a tool to categorize the goals set and the timeframe for the plan. Time Frame Self-Developmental Goals Self-Management Conceptualization Servant leaders seek to nurture their abilities to dream great dreams; not just consumed by achieving operational goals. To develop characteristic and thinking process encompass broader-based conceptual thinking require discipline and practice. Leading Others Influencing/Persuasion Servant leaders seek to persuade and convince others through inspiration rather than coerce compliance. This requires a level of confidence, personal drive and energy to be emulated to the followers. As represented in one of my weaknesses from the self-assessment, I lack in self-motivation, self-esteem and assertiveness. These characteristics need to be developed in order to gain enough personal power to lead and guide others. Innovation Creativity Creativity is one of the key characteristics of servant leaders. Also, the hospitality industry takes great importance in areas of innovation to stay competitive and relevant. This is a characteristic that continually needs to be fostered and developed. Social Responsibility Ethically Social Servant Leadership highlights the importance of leading for the greater good for a deeper moral purpose. This emphasizes the need for moral awareness and ethical conducts when leading. This can be done by participating more in charitable or environmental causes which aim in improving social welfare of the broader society. Such participation allow exposure and knowledge-gaining. Evaluation by Multi-Step Action Plan 1 year Completing Bachelor of Business Degree 3 years Employment in Airline as Flight Attendant to gain exposure to new experiences, ethical conducts and ideas and insight knowledge on providing service in hospitality industry (Innovation & Social Responsibility) 2 years Further study on Master of Hospitality Management to broaden conceptual thinking process. This also help to gain self-esteem and improve on the ability to influence (Conceptualization & Influencing) Working in Management VII. Industry Leader Input Previously I focused my goals only on the trait developments. This was difficult measure because characteristics can only be proven once I’ve been put on the position to be a leader in a group. There was no tangible achievement to evaluate the success of my goal planning. Therefore, through his suggestion, I modified my goal timeframe by adding a multi-step action plan that cover the length of time to achieve each target. For example, the employment in an Airline industry will help me garner new experiences, perspective and practice discipline in work ethics. Feedback on my work performance from supervisors can serve as a form of evaluation. Also, the attainment of higher qualification will allow me to gain broader and deeper knowledge on the industry through research. The exposure and experience may help me to develop a stronger leadership characteristic and further evaluation can be done through taking re-test for EI. Wordcount: 1,509 words (Excluding References, Appedices, Headings & Tables) VIII. Appendices 1. Michigan Leadership Competency Model Leadership Assessment Report Scores range from 1 to 6, with 1 indicating that you rated yourself low on that competency and 6 indicating that you rated yourself high. Introverted iNtuition Introverted intuitives, INFJs enjoy a greater clarity of perception of inner, unconscious processes than all but their INTJ cousins. Just as SP types commune with the object and â€Å"live in the here and now† of the physical world, INFJs readily grasp the hidden psychological stimuli behind the more observable dynamics of behavior and affect. Their amazing ability to deduce the inner workings of the mind, will and emotions of others gives INFJs their reputation as prophets and seers. Unlike the confining, routinizing nature of introverted sensing, introverted intuition frees this type to act insightfully and spontaneously as unique solutions arise on an event by event basis. Extraverted Feeling Extraverted feeling, the auxiliary deciding function, expresses a range of emotion and opinions of, for and about people. INFJs, like many other FJ types, find themselves caught between the desire to express their wealth of feelings and moral conclusions about the actions and attitudes of others, and the awareness of the consequences of unbridled candor. Some vent the attending emotions in private, to trusted allies. Such confidants are chosen with care, for INFJs are well aware of the treachery that can reside in the hearts of mortals. This particular combination of introverted intuition and extraverted feeling provides INFJs with the raw material from which perceptive counselors are shaped. Introverted Thinking The INFJ’s thinking is introverted, turned toward the subject. Perhaps it is when the INFJ’s thinking function is operative that he is most aloof. A comrade might surmise that such detachment signals a disillusionment, that she has also been found lacking by the sardonic eye of this one who plumbs the depths of the human spirit. Experience suggests that such distancing is merely an indication that the seer is hard at work and focusing energy into this less efficient tertiary function. Extraverted Sensing INFJs are twice blessed with clarity of vision, both internal and external. Just as they possess inner vision which is drawn to the forms of the unconscious, they also have external sensing perception which readily takes hold of worldly objects. Sensing, however, is the weakest of the INFJ’s arsenal and the most vulnerable. INFJs, like their fellow intuitives, may be so absorbed in intuitive perceiving that they become oblivious to physical reality. The INFJ under stress may fall prey to various forms of immediate gratification. Awareness of extraverted sensing is probably the source of the â€Å"SP wannabe† side of INFJs. Many yearn to live spontaneously; it’s not uncommon for INFJ actors to take on an SP (often ESTP) role. References Briggs, K. C., & Myers, I. B. (1998). Myers-Briggs Type Indicator. Palo Alto, CA. Greenleaf, R. K. (1977). The Servant as Leader. Business Leadership: A Jossey-Bass Reader. San Francisco: Jossey-Bass. Miller, Skringar, Dalglish & Stevens, (2012) Leadership and Change Management. 1st ed. Prahran VIC Australia: Tilde University Press. Maxwell, J. C., & Dorvan, J. (1997). Becoming a Person of Influence: How to Positively Impact the Lives of Others. Nashville: Thomas Nelson Schein, V.E. (2001) A global look at psychological barriers to women’s progress in management. Journal of Social Issues. 57, pp. 675-688. Schein, V.E., & Mueller, R. (1992). Sex role stereotyping and requisite management characteristics: A cross cultural look. Journal of Organizational Behavior. 13, pp. 439-447. Carli L.L., Eagly A.H. (1999). Gender effects on influence and emergent leadership Powell G.N. (Ed.), Handbook of gender and work, Sage, Thousand Oaks, CA, pp. 203–222 Soo Min Toh, Geoffrey J. Leonardelli (2012) Cultural constraints on the emergence of women as leaders. Journal of World Business, Vol. 47, Issue 4, pp. 604-611 Karmjit Singh (1984). Successful strategies—The story of Singapore Airlines (SIA) Long Range Planning, Vol.17, Issue 5, pp. 17-22 Dranitsaris, A., (ed.) 2009, Personality Type and Leadership Behaviour: Jung’s Typology for the Workplace, e-book, accessed 25 April 2013, Central Michigan University, 2004, Leadership Competency Model, accessed 20 April 2013, < http://www.chsbs.cmich.edu/leader_model/CompModel/EDUMAIN.htm > Heiss, M.M, Butt, J.,1999, INFJ, Typelogic, accessed 25 April 2013, HumanMetrics Jung’s Typology Test INFJ, 2012, accessed 25 April 2013,

Thursday, January 9, 2020

The Influence of Race and Ethnicity on a Persons...

Introduction I decided to write about the influence of race and ethnicity on a person’s educational level. I was born and raised in the Dominican Republic where, within my social group, schooling and education was deemed as an essential part of life. In the United States, however, there exist a greater number of racial and ethnic groups, and it is evident that an achievement gap exists among these groups. Here, Dominicans are marginalized as part of a Hispanic minority group that does not achieve the educational status of other groups, such as Whites or Jewish. I chose to write about the disparity of education within races and seek to answer how race affects a person’s educational level. Through research, I will examine if there is†¦show more content†¦This theoretical framework will help me to present and describe the theory, which explains why the research problem under study exists. According to sociologist there are two main views of inequalities within sociology. One view supports the functionalist theory and the other supports the conflict theory. I preferred to use both theories to help support my research. Ashley Crossman a sociologist says â€Å"Functionalist theorists believe that inequality is inevitable and desirable and plays an important function in society. In the other hand, conflict theory view inequality as resulting from groups with power dominating less powerful groups.†(Crossman, 2000). A functionalist theory perspective on education examines the society. Also, functionalist theories will emphasis on aspects such as schools, education, competition and equality of opportunity. These theories narrate and give structure to my topic. I will talk about the differences between races and the huge gap in education. The education can vary depending on the social capital status, the region of the country, culture, and races, among other variables. 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