Free Vibration Of A Cantilever Objective

Free Vibration Of A Cantilever Objective The purpose of this experiment is to determine the natural frequency of a cantilever beam study both undamped and damped free vibration motion of a cantilever beam. Vibration is the periodic motion of a body or system of connected bodies displaced from a position of equilibrium. In general, there are two types of vibration, free and forced. Free vibration is maintained by gravitational or elastic restoring force. Forced vibration is caused by an external periodic or intermittent force applied to the system. Both of these types of vibration may be either damped or undamped. Undamped vibrations can continue indefinitely because frictional effects are neglected in the analysis. Basically, if a system that is subjected to an initial disturbance and is left to vibrate on its own, the subsequent vibration is known as the free vibration. Vibrations without damping would result in a continuous vibration of the particular oscillatory body. As a matter of fact, it will produce a displacement-time graph of such nature as shown in the following figure. This graph is commonly referred to as the simple harmonic motion. http://upload.wikimedia.org/wikipedia/co mmons/4/44/Simple_harmonic_motion.png Figure 1: Simple Harmonic Motion (Displacement-Time Graph) However, in reality, just as with many other scientific theories, this is impossible because friction and other forces are present both internally and externally. As the system is subjected to these forces, this phenomena is called damping. The principle effect of damping is to reduce the amplitude of an oscillation, not to change its frequency. So, the graph of the amplitude of a normal damped oscillation might look like the following: http://www.efunda.com/formulae/vibrations/sdof_images/SDOF_UnderDamped_Response.gif Figure 2: Graph of Damped Oscillation (Displacement-Time Graph) Apparatus and Materials: 1. Cantilever beam apparatus -Modulus of elasticity of aluminium(E) : 70GPa -Dimension of the cantilever beam : 927mm (L) ÃÆ'- 19.09mm (W) ÃÆ'- 6.35mm (H) -Mass of the cantilever beam : 292.59g Mass of the damper : 122 g 2. Strain gauge 3. Strain recorder 4. Viscous damper Experimental Procedures: Figure 3: Experiment Setup without Viscous Damper Figure 4: Experiment Setup with Viscous Damper The computer and the strain recorder were switched on. The strain recorder application software was started by double clicking on the DC104REng shortcut icon on the computer desktop. The experiment setup was shown in Figure 3. The operation of the strain recorder and the recorder application software were referred to the operational manual. The viscous damper was removed if it was attached to the beam. The beam was held and displaced by, ymax, -20mm, -15mm, -10m, -5mm, 0, 5mm, 10mm, 15mm,and 20mm. The strain recorder reading for each displacement value from the Numerical Monitor screen of the application software was recorded manually. The relationship of the displacement (of the free end of the beam) and the strain recorder reading was obtained by plotting an appropriate graph using a spreadsheet. The beam is displaced by 30mm and the beam is left to vibrate on its own. The strain recorder reading was recorded by clicking on the Play and Stop button. The recorded file was retrieved by clicking on the Read USB button. The graph of the beam displacement versus time, t was plotted. The experiment was repeated by using beam displacement of 50mm. The viscous damper was connected as shown in Figure 3. Steps 7 and 10 were repeated by using beam displacement of 30mm and 50mm respectively. a) Theoretical Calculations As given in the experiment: Modulus of elasticity of aluminium,E = 70 GPa Length of the cantilever beam, L = 0.927m Width of the cantilever beam,b = 0.019m Thickness of the cantilever beam, h = 0.006m Mass of the cantilever beam, mcantilever = 0.293 kg Mass of the damper, mdamper = 0.122 kg b) Experimental Results and Calculations Free Vibration of Cantilever Beam at 30mm Displacement Natural Circular Frequency of Beam with Viscous Damper, The free vibration of the theoretical natural frequency of the cantilever beam in this experiment is 5.75Hz while the experimental natural frequency of the cantilever beam is 6.25Hz for amplitude of 30mm and 6.25Hz for amplitude of 50mm. The viscously damped vibration of the theoretical natural frequency of the cantilever beam is 3.45Hz and the experimental natural frequency of the cantilever beam for amplitude of 30mm and 50mm are 3.57Hz and 3.57Hz. Percentage error, % x 100% Free Vibration of Cantilever Beam at 30mm Displacement Percentage error, %= x 100% =8.70% Free Vibration of Cantilever Beam at 50mm Displacement Percentage error, %= x 100% =8.70% Viscously Damped Vibration of Cantilever Beam at 30mm Displacement Percentage error, %= x 100% =3.48% Viscously Damped Vibration of Cantilever Beam at 50mm Displacement Percentage error, %= x 100% =3.48% In this experiment, it is calculated that the percentage error for the free vibration is both 8.70% for 30mm and 50mm. For the viciously damped vibration, the percentage error for the 30mm and 50mm were both 3.48%. The results of the experiment were slightly inaccurate. This may be caused by the external force which is the air resistance as the beam oscillates. Another factor is caused by parallax error which occurred during the measuring of displacement before the beam was released as our eye level was not perpendicular to the scale of the metre rule. When the beam is released, it slightly hit the bottom of the container which decreases the original force released drastically which affects the amplitude of oscillation. Furthermore, the Modulus of Elasticity(Youngs Modulus) was given, which might not be accurate. All these source of error may affect the results of the experiment to be inaccurate. The results of the experiment can be improved by measuring the Modulus of Elasticity. Using a deeper container would also avoid the damper to hit the bottom of the container. Furthermore, the experiment can be done in a vacuum box to avoid air resistance. Eye level should be adjusted until it is perpendicular to the metre rule scale. This steps can increase the accuracy of the results. The damped period, damped natural frequency and the damping ratio of the system of free vibration is. When the amplitude is 30mm or 50mm for both cases, they have the same damped period, damped natural frequency and damped ratio. The percentage error for the free vibration of 30mm and 50mm were both 8.70% while for the viciously damped of 30mm and 50mm were both 3.48%. This indicates that the difference in amplitudes do not affect the frequency of the oscillation. From the general equation of frequency : , where c=speed of wave ÃŽÂ »= wavelength This formula proves that amplitude or displacement does not affect the frequency of the oscillation. If the strain gauge is mounted on the other end of the cantilever beam, the results would be not accurate as the gauge is very sensitive to changes. At the other end, there is not much difference in the change of length which affects the strain. In Figure 3, the strain can be detected more easily as the change in length is very obvious. This is because when the free end is free to vibrates, the vibration will be strong but the compression and tension that results on the surface of pressure sensor is not that strong. Conclusion : The theoretical natural frequency , for this experiment is 5.75Hz for free vibration cantilever. The value of both 30mm and 50mm frequency obtained were 6.25Hz which have percentage error of 8.70%. Whereas, the theoretical damped natural frequency , is 3.45 Hz. The value of both 30mm and 50mm frequency obtained were 3.57Hz which have percentage error of 3.48%. Furthermore, the results proves that the displacement does not affect the vibration(frequency) of the oscillation of the cantilever beam.

Essay on Camus’ The Stranger (The Outsider): Parallels Within

Parallels Within The Stranger (The Outsider) The Stranger by Albert Camus is a story of a sequence of events in one man's life that cause him to question the nature of the universe and his position in it. The book is written in two parts and each part seems to reflect in large degree the actions occurring in the other. There are curious parallels throughout the two parts that seem to indicate the emotional state of Meursault, the protagonist, and his view of the world. Meursault is a fairly average individual who is distinctive more in his apathy and passive pessimism than in anything else. He rarely talks because he generally has nothing to say, and he does what is requested of him because he feels that resisting commands is more of a bother than it is worth. Meursault never did anything notable or distinctive in his life: a fact which makes the events of the book all the more intriguing. Part I of The Stranger begins with Meursault's attendance at his mother's funeral. It ends with Meursault on the beach at Algiers killing a man. Part II is concerned with Meursault's trial for that same murder, his ultimate sentencing to death and the mental anguish that he experiences as a result of this sentence. Several curious parallels emerge here, especially with regard to Meursault's perception of the world. In Part I, Meursault is spending the night next to his mother's coffin at a sort of pre-funeral vigil. With him are several old people who were friends of his mother at the home in which she had been living at the time of her death. Meursault has the strange feeling that he can see all of their faces really clearly, that he can observe every detail of their clothing and that they will be indelibly impr... ...r has not done makes no essential difference at the end. The nurse at the funeral tells him, "if you walk too slowly, you'll get heat exhaustion, but if you walk too fast, then the cool air in church will give you a chill.† As he kills the Arab, he thinks, "Whether I fire or don't fire is irrelevant; the ending will be the same.† And at the trial, Meursault tells the prosecutor, "I have lived my life thus and did x, but if I had done y or z instead, it wouldn't have mattered.† And, ultimately, Meursault turns out to be correct; he discovers that when death approaches, all men are equal, no matter what their ages or previous lives. Meursault views death as an escape: you can't escape from it, but you can escape into it, and he prepares himself to do so, bit by bit. Each parellel incident is just one more winding round of the rope that will bind him completely.

Congressional Earmarks

In fiscal year 2008, there were 11,524 earmarks totaling $16,501,833,000 for appropriations accounts. A Congressional earmark is a provision that directs funds to be spent on specific projects. Congressional earmarks should be banned and the unused money should be returned to the citizens. The largest Disadvantage of congressional earmarks that I can see is the amount of money they use. An earmark on an Alaskan highway bill was for a bridge, that took money from hurricane reconstruction. This bridge would have cost $320 million. As federal taxpayers would you like to pay $320 million, by way of three separate earmarks? These three earmarks where added to the highway bill in 2005. These earmarks managed to take almost $223 million from a reconstruction project for a bridge in Louisiana. According to the 2010 copy of the Congressional Pig Book , it showed almost 9,200 earmarks totaling $16. 5 billion dollars. Even though that is a 10. % decline from 2009, the fact that we are trillions of dollars in debt and we are using the money to fund projects like the Monroe County Farmer’s Market in Kentucky and The second largest disadvantage that I can see from the use of earmarks is the humiliation and disgrace they can bring. The bridge above that is mentioned took money for hurricane reconstruction. This project is a humiliation to the people of Alaska and the U. S. Congress some people say. Some people view the bridge as an object of national ridicule and a symbol of the fiscal irresponsibility of many in Congress toward the money entrusted to them by the taxpayers. In response to this national humiliation, many in Alaska have vented their anger in the state's newspapers, and the papers' editors have also objected to the bridge on their editorial pages. According to http://www. heritage. org â€Å"David Raskin of Homer, Alaska, wrote, â€Å"Alaskans owe an apology to the people of New Orleans, to Alaska Native people and to the Nation for their selfish shortsightedness in sending these scoundrels to Washington and voting to keep them there. â€Å"†

Effects of domestic violence domestic abuse on women and children Essay

42% of women and 20% of men sustained minor injuries such as scratches, bruises, broken bones or pregnancy complications (Cathy Meyer, 2016). The result of domestic abuse does have long-term physical effects including digestive problems, hypertension or skin disorders (www.liveabout.com 15/11/17). Family members, especially children, can experience the physical effects of abuse even though they have not been harmed or touched. They can complain about stomach aches, headaches and could experience irregular bowel movements and wet the bed. Many women who have been abused find it difficult to concentrate on their daily activates because of the effects of domestic abuse as they are constantly on edge. If a person is experiencing domestic abuse this can be physical as well as emotional and if the abuse is constant then regular hospital visits and rest days will be needed for a recovery if the person has a job day off will be needed and too many could lead to the person eventually being let off. When children experience domestic violence sometimes they feel confused or it’s their fault. If the violence or arguments takes place at night, it can be very distracting for the child to be able to sleep as they are constantly hearing the abuse given. This could affect their education as they will be tired and have poor concentration, affecting progress. Domestic abuse will have an effect on the victim’s emotional health as it makes them feel a range of emotions, such as anxiety, low self-esteem, suicidal thoughts or could cause a post-traumatic distress which includes unwanted flashbacks , nightmares or uncontrollable thoughts (www.joyfulheartcondition.org). Children who are exposed to domestic violence in their home could develop anxiety, fearing they might be left with the abusive parent who will then take their abuse out on them. Depression is also an emotion that most people will experience as they feel helpless and powerless. This is known to be more common in girls as boys tend to act out with aggression. Alisha Dixon, in the BBC Documentary â€Å"Don’t Hit My mum†, many children feel guilt that they could not prevent the abuse. Children may not want to leave the house in case their parent is unsafe. I found evidence to back this is on saying children will become clingy and not want to leave mum or dad and they feel they have a responsibility for to protect them. When in a domestic violent relationship, it is knowing that the partner will try to control the other person’s life by constantly knowing what they are doing and persuading or telling the victim they cannot go places when they really want to go. This will affect their relationship with family or friends causing the victim to never see them eventually leading them into isolation. Other social behavior includes aggressive behavior and poor social skills, meaning they could not make any friends as their social skills are poor. Bereavement A person dying close to you is hard both on adults and children. They can experience the same feelings as they are going through the same things however someone who is of an older age may be able to deal with the effects in a more mature manner, they will find that their energy levels will be very low as they will have a feeling f numbness inside them. If their energy is low, they will not go out and do daily activities which could lead them to stress and anxiety. Dealing with death and not everyone likes to be around people especially not in a work or school environment. This means that they will be missing out on important days in work or school causing them to fall behind building up more stress and anxiety that version does not need. When people describe losing a loved one they usually describe their self as being numb. Which is a normal defense mechanism of the mind to help you from being overwhelmed with emotions? Other people may experience guilt or anxiety

Free Essays on HEROISM-DAD

When I hear the word hero, the first person who comes to mind is my father, Raymond Mathers. He defines every part of the word â€Å"hero†. He is a good father and a dedicated teacher of life. He saved his own life, and mine. My father has overcome a countless number of obstacles. Raymond Ledoux was born in New Bedford, Massachusetts on August 17, 1950. When his high school years were coming to an end, bad crowds introduced him to all sorts of drugs and alcohol. This started a horrible beginning to a long road of struggles. Although New Bedford is the â€Å"heroin capital† of New England, the interest of substance started in a visit to Florida. Coke, marijuana, heroin, alcohol and cigarettes were all vices in my father’s life. A coke deal in Ft. Lauderdale is the romantic story of how my parents met each other. Looking beyond all of the negative aspects taking up there lives; they were in love and wanted to start a family. At the age of thirty-eight, Ray had a baby girl that goes by the name of Jamie-Rae Ledoux. Our family moved back to New England and my parents were looking to straighten out there lives for there baby and themselves. My father finally realized that staying with my mother was making the process longer and more difficult so he left with all positive intentions. Once living on his own, he defeated all bad habits on his own. He stopped drinking, smoking cigarettes, and all drug use; including the methadone he was on which was supposed to help stop the drug and alcohol addictions themselves. There were not any AA meetings, drug counseling, or nicotine patches; he quit every addiction with his own willpower. In the mean time I was living with my mom, who was still abusing alcohol and drugs. My father knew it wasn’t anything a child needed to experience. He wanted me to grow up in a safe, loving, and substance-free home. As a result, he bought a house and took me out of the negative environment my mother provided. I ... Free Essays on HEROISM-DAD Free Essays on HEROISM-DAD When I hear the word hero, the first person who comes to mind is my father, Raymond Mathers. He defines every part of the word â€Å"hero†. He is a good father and a dedicated teacher of life. He saved his own life, and mine. My father has overcome a countless number of obstacles. Raymond Ledoux was born in New Bedford, Massachusetts on August 17, 1950. When his high school years were coming to an end, bad crowds introduced him to all sorts of drugs and alcohol. This started a horrible beginning to a long road of struggles. Although New Bedford is the â€Å"heroin capital† of New England, the interest of substance started in a visit to Florida. Coke, marijuana, heroin, alcohol and cigarettes were all vices in my father’s life. A coke deal in Ft. Lauderdale is the romantic story of how my parents met each other. Looking beyond all of the negative aspects taking up there lives; they were in love and wanted to start a family. At the age of thirty-eight, Ray had a baby girl that goes by the name of Jamie-Rae Ledoux. Our family moved back to New England and my parents were looking to straighten out there lives for there baby and themselves. My father finally realized that staying with my mother was making the process longer and more difficult so he left with all positive intentions. Once living on his own, he defeated all bad habits on his own. He stopped drinking, smoking cigarettes, and all drug use; including the methadone he was on which was supposed to help stop the drug and alcohol addictions themselves. There were not any AA meetings, drug counseling, or nicotine patches; he quit every addiction with his own willpower. In the mean time I was living with my mom, who was still abusing alcohol and drugs. My father knew it wasn’t anything a child needed to experience. He wanted me to grow up in a safe, loving, and substance-free home. As a result, he bought a house and took me out of the negative environment my mother provided. I ...

WK 5 Strategic Philanthropy for Organizations Term Paper

WK 5 Strategic Philanthropy for Organizations - Term Paper Example Strategic Philanthropy refers to the practice of organizations in which they channel their charitable activities towards specific course that is expected to benefit their organizational objectives. In this course, philanthropy is a means used by different firms to benefit other organizations while advancing their business interests at the same time. Strategic philanthropy is associated with organizations and not individuals thus executed by the top management of organizations such as the board of directors and several departments. Philanthropy plays an important role in developing and retaining customer loyalty. According to Fioravante (2010), eighty percent of Americans are more loyal to an organization that contribute towards course that they have interest. Moreover, Valor (2007), survey demonstrated that most consumers have greater trust for companies that are associated with certain kind of social activities that give back to community. Increased customer loyalty have indirect benefits such as increased customer satisfaction, increased productivity and quality, employee commitment, profitability and reduced legal and regulatory interventions. For example, GTE greatest concerns are technology and literacy; hence the organization through its foundation distributed $30 million in 1999 (Debbie & Ferrell, 2002). Strategic philanthropy target customers’ concerns and interests in provision of resources that aim at building trust. As stated by Valor (2007), enhancing trust and acceptability among the consumers can be achieved through developing strong consumer loyalty thus gaining competitive advantage. Coca-cola has always linked its operating practices and resources with the stakeholders concerns. For example, the company has channeled not only its resources but also expertise to environmental issues. According to Debbie & Ferrell (2002), the company has provided expertise and financial support to organizations that

Criminal Justice Essay Example | Topics and Well Written Essays - 1000 words - 1

Criminal Justice - Essay Example As a result, the needs of the female prisoners are often disregarded thus negatively affecting their mental and physical health in the process. It has also been observed that the failure to meet the needs of the female prisoners deprives them of their right to basic dignity and leads to the violation of their fundamental human rights (Law and Whitehorn, 2012). Some of the key issues commonly faced by female prisoners include custodial sexual misconduct; caring for their children; lack of availability of adequate healthcare facilities suited for their needs; lack of accessible services; vulnerability to abuse; etc among others. The needs and concerns of female prisoners are starkly different as compared to their male counterparts, a fact which has been largely ignored so far. Unlike men, the female prisoners are solely responsible for caring for their young children. In such a situation, isolation due to confinement inevitably takes a toll on their mental health. Furthermore they are relatively more vulnerable to abuse and neglect in prison due to the differences in the sexual and reproductive health as compared to males. Issues such as these are hence likely to aggravate the mental and health problems faced by them (UN Office of Drugs and Crime, 2008). Women are also found to be highly vulnerable to prison abuse (Clear, Reisig, and Cole, 2012). Their mental health in particular is far more likely to deteriorate while in confinement due to factors such as overcrowding, lack of proper assessment procedures, discomfort on account of being supervised by male staff, etc (McElreath, Keena, Elter and Stuart, 2011; Stohr, Hemmens, and Walsh, 2008). Furthermore it has also been observed by various researchers that women are more prone to attempt suicide while in confinement due to mental stress and trauma, and lack of availability of appropriate healthcare facilities to address their specific healthcare needs (Petersilia and Reitz, 2012). Critical evaluation: There has been a significant rise in the number of female prisoners in the United States during the past two decades. This sudden increase of female offenders can largely be contributed to stricter punishment and longer incarceration for drug offenders, as a part of the war on drugs campaign. Thus, the policies introduced by the administration to eliminate and / or reduce the disparities in sentencing, ultimately led to the rise of female inmates behind bars (Stange, Oyster, and Sloan, 2011; Miller, 2009). According to the American Civil Liberties Union, women comprise of the fastest growing segment of the incarcerated population, increasing at nearly double the rate of men, in the United States (ACLU, 2007). There is substantial evidence indicating the substantial over-representation of women of color in the American prisons as well as the criminal justice system, with Blacks and Hispanics comprising of the largest female population behind bars (Law and Whitehorn, 2012; Oberman and Meyer, 20 08). Some of the key reasons behind the increased incarceration rates of females belonging to the minority population include poverty, and unemployment which significantly hampers their ability to provide and care for their families. Their demographic and socio-economic background makes them highly prone to commit economically driven crimes such as property crimes, prostitution and at times drug