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.

Me And Her :: essays research papers

We have been dating for 1 month and 8 days. Able to have her as a girlfriend is the greatest gift of all. Thinking back, I still can't figure out, what gave me the courage to ask her out, maybe it was my determine mind, which constantly reminds me that i want her. On the first day of our relationship, everything seemed normaly, too normal it made me think that we will never go beyond friends. That thought actually scared me a little, because it was like having something you have always wanted, but you can't hold on to it. We didn't get the chance to speak to each other the next day. I guess she found me too boring, or maybe she too, think that there's no way we are goign to go further than typical friends could. At that point, I did have the thought of letting her go, because I felt very unloved. On the same night I got to talk to Katherine, she was the girl i use to like. "Use to"?? Does that mean I dont' like her anymore? I don't know the answer to that question. At least I believe the answer is not important at that stage. Because what she said later on during our convesation, is what i considered to be most important. She said that she like me more than a friend. I was flattered, when i heard those words. I was happy and sad simultaneously. Happy because I have found someone that might love me. Sad because that person isn't my girlfriend. I did ask myself serveral times, why did those words came out of Katherine's mouth and not her's? But that question didn't stay in my head for long, because another question came up, and I believe this coming question is the most important one, and must be answered immediately. "Should I choose Katherine or my current girlfriend?" I was a confusing situation, even though half an hour ago I said that I was prepared to leave my girlfriend, I guess its true, that you won't know, how important someone or something is to you, until you are at the edge of losing them. A couple of days had gone by, I still haven't decided who i want. During this last couple of days, I didn't talk to Katherine, instead I talked to my girlfriend and told her the whole situation.

Illegality and Various Consequences Essay

ILLEGALITY A contact to be legally binding it should be legal. The contracts which are against the law or the public policy are consider as illegal contracts. Courts do not enforce illegal contracts and treated as void contracts. There are four major criteria to decide the illegality of a contract. Contracts declared illegal by statute law. Statute law consists of both statutes and ordinance which had been legislated by the parliament of the country. Every contact should adhere to the statutes prepared by the parliament. If an element of a contract exceeded any statue that contract becomes illegal. A contract does not need to be a criminal offence in order to be decided as an illegal contract. For an example if there is a minimum price placed for a certain product by a statute such as â€Å"consumer protection act† and when a contract that goes beyond the price element fixed by the statute, then it becomes illegal thus court can void such a contract. Contracts that go against common law. In Sri Lanka, the Roman-Dutch law is considered as the common law. It is important to note that Roman-Dutch law only acts as a residuary law which contents only five present of the contract law. In respect of the three civil marriage laws, that is andyan marriage law Muslim marriage law and thesawalame law the Roman-Dutch law acts as a residuary law. That means regarding a particular issue, if three local laws are silent, Roman-Dutch law comes to enact as a residuary law. And some of the property always belongs to the government. Which means no can claim, own or destroy? Some recourse, for an example costs, forest and rivers always remain with state. Therefore if two parties get together and carried out a contract to cut-down trees in a forest, it becomes illegal since such a contract goes beyond the common law. Contracts void for being against the public policy. Sometime there may be situations where contracts may not break any laws but still they may become declared illegal due to the fact that such contracts violate the acceptable public policy. Therefore courts do not permit to form contracts which go against the public policy. However the term public policy is merely a legal term and does not indicate that it is related to existing government policies. In addition courts have prepared a list of contracts which are deemed to be opposed to public policy : a) Agreement for stifling precision and for outing Jury diction of courts are unlawful not enforceable. ) Agreement in fraud of insolvency law is illegal. d) Agreement for using improper influence of any kind with Judge or officer of justice is void. e) Agreement in restraint of the marriage of any person other then a minor is void. f) Agreement to procure marriage for reward is void. g) Agreement to pay money to parent or guardian in consideration of giving his daughter in marriage I void. Similarly, a promise by the bride’s Parent to pay money to the bridegroom or his parent I illegal. h) Traffic by ay of ale in public office and Appointment or title for monetary consideration I illegal. ) Agreement tending to create monopoly are void. j) Agreements in restraint of trade are void, partial restraint I allowed in sale of Goodwill. k) Contract unduly retrain individual liberty are enforceable. [http:// www. reportbd. com/articles/42/1 Noid-Contract/Page1 . html ] Contracts that go against the morality. Morality is the quality of being in accord with standards of right or good conduct or a system of ideas that fall into those same categories. [http:// www. allaboutphilosophy. org/definition-of-morality-faq. htm ]. Morality is depending on the culture, religion and other traditions in a country. It can be varies from country to country due to this reason. Morality is much broader than the statutory law. And when a contract is made it should adhere within the accepted morality and should not go against it. Courts can void such contracts that go against the morality. For an example when there is a relationship between an unmarried woman and a married person and if the particular woman decided to break their relationship, that particular person cannot take any legal actions against that woman ever since the promise of marriage contract between them is against the orality and thereby courts may declare it as an illegal contract which is voidable. Consequences of illegality. Enturpi Cauza If one is engaged in illegal activity, one cannot sue another for damages that arose out of that illegal activity. [http://www. duhaime. org/LegalDictionary/E/ Exturpicausanonorituractio. spx ]. In other words this means that if the contract is illegal such contracts are considered as void thus no legal consequences arise under this. This is because of the fact that courts do not enforce illegal contracts and even cannot be accepted for hearing at the court. Inpari Delicto Legal principle that if two parties in a dispute are equally at fault then the party in posse ssion of the contested property gets to retain it (courts will not interfere with breach of a contract, or which fails to take appropriate action (or takes inappropriate action) to limit or recoup a loss, may not claim damages. http:// www. businessdictionary. com/definition/in-pari-delicto- doctrine. html#ixzzOyxs2Napo]. Courts may accept some illegal cases under this rule. If the plaintiff is equally guilty as the defendant, the courts may hear the case and may provide remedies to the defendant. This is due to the fact that Inpari Delicto eemed that if the both parties are equally responsible for the illegality, then the defendant is in a stronger position whereas courts do not support the plaintiff to recover anything from the defendant. However there are some exceptions to the Inpari Delicto rule where the court may favors the plaintiff : 01). Where the guilt of the parties is not equal. When there is a possibility to prove that the guilt of the plaintiff is less than the guilt of the defendant, courts sometime may provide the remedies for the plaintiff. This could be happen if the plaintiff is able to prove that there is a mistake in the facts ade by the defendant at the time of making the contract. In such a scenario court may order the plaintiff to recover any money paid or should receive despite the fact that contract is illegal in nature. 2). Where the illegal activity substantially unperformed. This occurs when the illegal purpose of the contract is not carried out because one of the parties to the contract repents in time and prevents the illegal act to be executed any further. In such a case, the party who stopped the act to be carried out will be able to recover anything which he has paid to the other party . However this could be chievable only if it takes place when it would still have been possible to perform the contract. If the illegal purpose could not be realize for some reason that is out side the control of the plaintiff, he will not be able to recover the payment from the other party. 03). Unjust enrichment. The law only permits the persons to be rich in Just and acceptable ways. Law does not endure unjust enrichments. Therefore if the plaintiff is able to prove that the defendant has become rich in unjust ways due to the conduct of this contract, court may order the defendant to return the property that has acquired.

Learning to Cope with ADHD as an Adult Learner Essay

Learning to Cope with ADHD as an Adult Learner Typically when one hears the term â€Å"ADHD† and the potential negative effects that it could have on someone striving towards academic success, they immediately think school age children. Though it is more common for children to be diagnosed and treated, 5% of U.S. adults are living with this condition (American Psychiatric Association, 2012). First ADHD must be defined before coping methods can be explained. ADHD or Attention Deficit Hyperactive Disorder is a diagnosis applied to children and adults who consistently display certain characteristic behaviors such as distractibility (poor sustained attention to tasks), impulsivity (impaired impulse control and delayed gratification), and†¦show more content†¦Of those stimulant medications, the most common are Ritalin, Dexedrine, Adderall, Adderall XR, Concerta, Vyvanse, and Focalin XR (Jaksa, 1998). For those who do not like stimulant medications or the idea of seeing a psychiatrist on a regular basis, there are alter nate forms of treatment for dealing with the effects of ADHD. Yoga, Vitamins, Herbal Supplements, and even special diets have been proven to be successfully in helping an individual deal with the effects of ADHD (Mayo Clinic Staff, 2013). One could gain a lot from using these alternate forms of treatment if they want to take natural approach to treatment. They would not have to worry about the potential negative side effects of stimulant medications. They can also become addictive. However, this can also be risky. These alternate forms of treatment cannot replace the expertise and knowledge of a licensed psychiatrist. Working with someone who is certified to diagnose and treat this condition can provide access to some of the best treatment possible. ADHD is associated with poor grades, poor reading and mathematics standardized test scores, and an increased likelihood of repeating a school year (Daley Birchwood, 2009, pg. 457). The same academic challenges an individual faces as a c hild could carry over into adulthood and create similar challenges as an adult learner. Individuals with ADHD face academic disadvantages. This is not saying that an individual with ADHD cannot be the top student inShow MoreRelatedPsychology And Medication : Are Children Being Misdiagnosed And Over Medicated1334 Words   |  6 PagesChildren is not the Right Thing to do There are many types of people who may have Attention Deficit Disorder, also known as ADD/ADHD, which is attention deficit hyperactivity disorder. ADD is defined as learning disorder affecting children, adolescents, and some adults. Common symptoms of ADD are learning and behavioral difficulties as well as the typical problem of ADHD, hyperactivity. 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