lab21麻省理工研究生试卷
2021MBA英语真题英语
2021年研究生入学统一考试试题（英语二）Section I Use of EnglishDirections：Read the following text. Choose the best word (s) for each numbered blank and mark A, B, C or D on the ANSWER SHEET. (10 points)Why do people read negative Internet comments and do other things that will obviously be painful? Because humans have an inherent need to 1 uncertainty, according to a recent study in Psychological Science. The new research reveals that the need to know is so strong that people will 2 to satisfy their curiosity even when it is clear the answer will 3.In a series of four experiments, behavioral scientists at the University of Chicago and the Wisconsin School of Business tested students' willingness to 4 themselves to unpleasant stimuli in an effort to satisfy curiosity. For one 5 each participant was shown a pile of pens that the researcher claimed were from a previous experiment. The twist?Half of the pens would 6 an electric shock when clicked.Twenty-seven students were told which pens were electrified;another twenty-seven were told only that some were electrified 7 left alone in the room, the students who did not kn ow which ones would shock them clicked more pens and incurred more shocks than the students wh o knew what would 8 .Subsequent experiments reproduced this effect with other stimuli, 9 the sound of fingernails on a chalkboard and photographs of disgusting insects.The drive to 10 is deeply rooted in humans,much the same as the basic drives for 11 or shelter,sa ys Christopher Hsee of the University of Chicago. Curiosity is often considered a good instinct-it can 12new scientific advances, for instance-but sometimes such 13 can insight that curiosity can drive you to do 14 things is a profound curiosit y is possible to 15 ,however. In a final experiment,participants who were encouraged to 16 how they would feel after viewing an unpleasant picture were less likely to 17 to see such an results suggest th at imagining the 18 of following through on one's curiosity ahead of time can help determine 19 it is worth the endeavor. Thinking about long-term 20 is key to reducing the possible negative effects of curiosity."Hsee other words,don't read onli ne comments.1. A. resolve B. protect C. discuss D. ignore. refuse B. wait C. seek D. regret. rise B. last C. mislead D. hurt. alert B. tie C. expose D .treat. message B. trial C. review D. concept. remove B. weaken C. deliver D. interrupt7. A. Unless B. If C. Though D. When8. A. happen B. continue C. disappear D. change9. A. rather than B. such as C. regardless of D. owing to10. A. disagree B. forgive C. forget D. discover11. A. pay B. marriage C. food D. schooling. begin with B. rest on C. learn from D. lead to. withdrawal B. inquiry C. persistence D. diligence. self-destructive B. self-reliant C. self-evident D. self-deceptive. resist B. define C. replace D. trace. predict B. overlook C. design D. conceal17. A. remember B. choose C. promise D. pretend18. A. relief B. plan C. outcome D. duty. whether B. why C. where D. how20. A .limitations B. investments C. strategies D. consequencesSection Ⅱ Reading ComprehensionPart ADirections:Read the following four texts. Answer the questions below each text by choosing A, B, C or D. Mark your answers on the ANSWER SHEET. （40 points）Text 1It is curious that Stephen Koziatek feels almost as though he has to justify his efforts to give his students a better future.is part of something pioneering. He is a teacher at a New Hampshire high school where learning is not something of books and tests and mechanical memorization, but practical. When did it become accepted wisdom that students should be able to name the 13th president of the United States but be utterly overwhelmed by a broken bike chain?As Koziatek knows, there is learning in just about everything. Nothing is necessarily gained by forcing students to learn geometry at a graffitied desk stuck with generations of discarded chewing gum. They can also learn geometry by assembling a bicycle.But he’s also found a kind of insidious prejudice. Working with your hands is seen as almost a mark of inferiority. Schools in the family of vocational education “have that s tereotype, that it’s for kids who can’t make it academically,” he says.On one hand, that viewpoint is a logical product of America’s evolution. Manufacturing is not the economic engine that it once was. The job security that the US economy once offered to high school graduates has largely evaporated. More educationis the new principle. We want more for our kids, and rigitfully so.But the headlong push into bachelor’s degrees for all -and the subtle devaluing of anything less-misses an important point: That’s not the only thing the American economy needs. Yes, a bachelor’s degree opens more doors. But even now, 54 percent of the jobs in the country are middle-skill jobs, such as construction and high-skill manufacturing. But only 44 percent of workers are adequately trained.In other words, at a time when the working class has turned the country on its political head, frustrated that the opportunity that once defined America is vanishing, one obvious solution is staring us in the face. There is a gap in working-class jobs, but the workers who need those jobs most aren’t equipped to do them. Koziatek’s Manchester School of Technology High School is trying to fill that gap.Koziatek’s school is a wake-up call. When education becomes one-size-fits-all, it risks overlooking a nation’s diversity of gifts.21. A broken bike chain is mentioned to show students’ lack of______.A. mechanical memorizationB. academic trainingC. practical abilityD. pioneering spirit22. There exists the prejudice that vocational education is for kids who______.A. are financially disadvantagedB. are not academically successfulC. have a stereotyped mindD. have no career motivation23. We can infer from Paragraph 5 that high school graduates______.A. are entitled to more “educational privilegesB. are reluctant to work in manufacturingC .used to have more job opportunitiesD. used to have big financial concerns24. The headlong push into bachelor’s degrees for all_____.A. helps create a lot of middle-skill jobsB. may narrow the gap in working-class jobsC. is expected to yield a better-trained workforceD. indicates the overvaluing of higher education25. The author’s attitude toward Koziatek’s school can be described as_____.A. supportiveB. disappointedC. tolerantD. cautiousText2While fossil fuels- coal, oil, gas- still generate roughly 85 percent of the world's energy supply, it's clearer than ever that the future belongs to renewable sources such as wind and solar. The move to renewables is picking up momentum around the world: They now account for more than half of new power sources going on line.Some growth stems from a commitment by governments and farsighted Business to fund cleaner energy sources. But increasingly the stories about the plummeting prices of renewables, especially wind and solar. The cost of solar panels has dropped by 80 percent and the cost of wind turbines by close to one-third in the past eight years.In many parts of the world renewable energy is already a principal energy source. In Scotland, forexample, wind turbines provide enough electricity to power 95 percent of homes. While the rest of the world takes the lead, notably China and Europe, the United States is also seeing a remarkable shift. In March, for the first time, wind and solar power accounted for more than 10 percent of the power generated in the US ,reported the US Energy Information Administration.President Trump has underlined fossil fuels - especially coal - as the path to economic growth. In a recent speech in Iowa, he dismissed wind power as an unreliable energy source, But that message did not play well with many in Iowa, where wind turbines dot the fields and provide 36 percent of the state's electricity generation - and where tech giants like Microsoft are being attracted by the availability of clean energy to power their data centers.The question “what happens when the wind doesn't blow or the sun doesn'tshine?" has provide d a quick put-down for skeptics. But a boost in the storage-capacity of batteries is making their ability to keep power flowing around the clock more likely.The advance is driven in part by vehicle manufacturers, who are placing big bets on battery-powered electric vehicles. Although electric cars are still a rarity on roads now, this massive investment could change the picture rapidly in coming years.While there's a long way to go, the trend lines for renewables are spiking. The pace of change in energy sources appears to be speeding up perhaps: just in time to have a meaningful effect in slowing climate change. What Washington does-or doesn't do- to promote alternative energy may mean less and less a time of a global shift in thought.26. The word "plummeting"(Line 3, is closest in meaning to ______A. stabilizingB. changingC. fallingD. rising27. According to Paragraph 3, the use of renewable energy in America ______A. is progressing notablyB. is as extensive as in EuropeC. faces many challengesD. has proved to be impractical28. It can be learned that in Iowa,______.A. wind is a widely used energy sourceB. wind energy has replaced fossil fuelsC. tech giants are investing in clean energyD. there is a shortage of clean energy supply29. Which of the following is true about clean energy according to Paragraphs 5&6?A. Its application has boosted battery storage.B. It is commonly used in car manufacturing.C. Its continuous supply is becoming a reality.D. Its sustainable exploitation will remain difficult.30. It can be inferred from the last paragraph that renewable energy _____.A. will bring the US closer to other countriesB. will accelerate global environmental changeC. is not really encouraged by the US governmentD. is not competitive enough with regard to its costText 3The power and ambition of the giants of the digital economy is astonishing —Amazon has just announced the purchase of the upmarket grocery chain Whole Foods for $, but two years agoFacebook paid even more than that to acquire the WhatsApp messaging service, which doesn’t have any physical product at all. What WhatsApp offered Facebook was an intricate and finely detailed web of its user s’ friendships and social lives.Facebook promised the European commission then that it would not link phone numbers to Facebook identities, but it broke the promise almost as soon as the deal went through. Even without knowing what was in the messages, the knowledge of who sent them and to whom was enormously revealing and still could be. What political journalist, what party whip, would not want to know the makeup of the WhatsApp groups in which Theresa May’s enemies are currently plotting? It may be that the value of Whole Foods to Amazon is not so much the 460 shops of owns, but the records of which customers have purchased what.Competition law appears to be the only way to address these imbalances of power. But it is clumsy. For one thing, it is very slow compared to the pace of change within the digital economy. By the time a problem has been addressed and remedied it may have vanished in the marketplace, to be replaced by new abuses of power. But there is a deeper conceptual problem, too. Competition law as presently interpreted deals with financial disadvantage to consumers and this is not obvious when the users of these services don’t pay for them. The users of their services are not their customers. That would be the people who buy advertising from them —and Facebook and Google, the two virtual giants, dominate digital advertising to the disadvantage of all other media and entertainment companies.The product they’re selling is data, and we, the users, convert our lives to data for the benefit of the digital giants. Just as some ants farm the bugs called aphids for the honeydew they produce wheto Paragraph1，Facebook acquired WhatsApp for its 。
麻省理工数学真题答案解析
麻省理工数学真题答案解析作为世界顶尖的科学技术机构之一，麻省理工学院的数学课程一直备受瞩目。
其数学考试着重培养学生的综合分析能力和解决问题的能力，因此，麻省理工数学真题对于广大数学爱好者来说具有参考价值。
在本文中，我们将通过解析一道麻省理工数学真题，探讨该题的解法和答案，帮助读者更好地理解数学思维和应用。
让我们先来看一道典型的麻省理工数学真题：题目：某城市一年365天，每一天的天气要么是晴天要么是雨天。
如果没有任何规律可循，每一天的天气状况是独立且随机的。
已知该城市每年的晴天和雨天的比例为3:2，假设每个月有30天，请问该城市在某一月份中连续五天的天气都是晴天的概率是多少？解析：首先，我们需要了解一些基本概念。
题目中给出了该城市每年的晴天和雨天的比例为3:2，也就是说每年有5n天是晴天，3n天是雨天，其中n是任意正整数。
又已知每个月有30天，所以我们可以确定每个月的晴天和雨天的天数分别为18n和12n。
现在，我们的目标是求解该城市某一月份中连续五天都是晴天的概率。
为了做到这一点，我们需要找到这种情况可能出现的具体组合。
假设某个月的晴天和雨天分别用字母"S"和"R"表示，例如，连续五天都是晴天可以表示为"SSSSS"。
为了找出可能的组合，我们可以将连续五天的天气情况分为两类，一类是当第一个和最后一个都是晴天时，另一类是当第一个和最后一个都是雨天时。
对于第一类情况，我们可以从该月的第一天开始，连续五天都是晴天的概率为(18n/30) * (18n/30) * (18n/30) * (18n/30) *(18n/30)。
这里的18n/30表示某一天是晴天的概率。
因为每一天的天气状况是独立且随机的，所以连续五天都是晴天的概率可以通过连续五个晴天的概率相乘得到。
对于第二类情况，与第一类情况类似，我们可以从该月的第一天开始，连续五天都是雨天的概率为(12n/30) * (12n/30) * (12n/30) * (12n/30) * (12n/30)。
2021年研究生英语模拟试卷与答案解析(15)
2021年研究生英语模拟试卷与答案解析15一、单选题(共40题)1.Recognizing when a friend or colleague feels sad,angry or surprised is key to getting along with orhers.1 a new study suggests that a skill for listening in on feelings may sometimes come with an extra dose of stress.This and other research 2 the prevailing view that emotional intelligence is uniformly 3 to its bearer.In a study published in the September 2021 issue of E7notion,psychologists Myriam Bechtoldt and Vanessa Schneider asked 166 male university students a series of questions to 4 their emotional smarts.5,they showed the students photographs of people's faces ancl askecl them 6 what extent feelings such as happiness or disgust were being expressed.The students 7 had to give job talks in front of judges displaying stern facial expressions.The scientists measured concentrations of the stress hormone cortisol in the students'saliva before and after the talk.In students who were 8 more emotionally intelligent,the stress measures increased more during the experiment and took 9 to go back to baseline.The 10 suggest that some people may be too emotionally clever for their own good,says Hillary Anger Elfenbein,a professor of organizational behavior at Washington University inSt.Louis."Sometimes you can be so good at something 11 it causes trouble,"she notes.Indeed,the study adds to previous research hinting at a（n）12 side of emotional intelligence.A study published in 2002 in Pers'onalr.t,y and Individual Di f ferences suggested that emotionally 13 people might be particularly 14 to feelings of depression and hopelessness.15,several studies,including one published in 2013 in PLOS ONE,have implied that emotional intelligence can be used to manipulate others for personal 16.More research is needed to see how exactly the relation between emotional intelligence and stress woulcl 17 0ut in women anclin people 18 different ages and education levels.19,emotional intelligence is a useful skill to have,as long as you learn to also properly 20 emotions-both others'and your own.8选？A：labeledB：perceivedC：ratedD：acknowledged【答案】：C【解析】：本题考查上下文语义一动词词义辨析。
MIT微观试卷exam1_topics
Topic Review: 14.04 MidtermI. Consumer Thoery: 75-85% of TestA. Construction of Utility Functions1.Requirements for the construction of a utility function2.Requirements for budget exhaustion3.Proving Convexity and Monotinicity of indifference curves (Two Good Case)4.Ordinal vs Cardinal Preferences5.Requirements for vNM utility functions (Expected Utility)B. Utility Maximization1.Utility Maximization/Indirect Utility Functions2.Expenditure Minimization3.Marshallian/Hicksian Demand Functions4.Envelope Theorem (Shephard’s Lemma)5.Kuhn-Tucker Optimization (At least know how to formally solve quasi-linear,leontieff, linear, Cobb Douglas. Problems will be similar, but not exactly thesame as these)6.Marginal Rate of Substitution – testing boundary conditions7.Intertemporal ChoiceC. Manipulations of Utility Functions1.Properties of the Indirect Utility/Expenditure Functions2.Finding the expenditure function from indirect utility3.Finding Hicksian/Marshallian Demand from indirect utility/expenditure4.Recovering one Hicksian Demand from another5.Moving from Marshallian Demand -> Hicksian Demand6.Constructing Utility functions from Indirect Utility7.Money Metric Utility Functions8.Properties of the Slutsky Matrix, properties of the symmetric matrix (Secondderivates of expenditure function)D. Choice1.Income and Substitution Effects2.Construction of the Slusky Matrix (With and Without Endowments)3.Inferior Goods, Giffen Goods4.WARP, GARP.5.Recovering preferences from choicesE. Aggregation1.Construction of Demand Curves2.Homothetic utility Functions (Form of expenditure function, properties of slutskymatrix)3.Aggregation across goods4.Gorman FormF. Uncertainty1.Properties necessary for vNM utility functions2.Affine Transformations3.Risk Aversion, Risk Neutral, Risk Loving4.Absolute, Relative risk aversion5.Certainty Equivalent6.Risk Premium7.Simple InsuranceII. Production 15-25% of testA. Technology1.Isoquants, Technical Rate of Substitution2.CRTS, DRTS, IRTS3.Production possibility frontier4.Short Run/Long Run ConstraintsB. Profit Maximization1.Setting up and solving profit maximization problems2.Testing for firm shut down3.WAPM4.Cost Minimization <-> Profit Maximization5.Factor Demands6.Supply FunctionC. Cost Minimization1.Techniques for minimizing costs2.Multiple Plant Problems3.Marginal Costs4.Sunk Costs5.Cost function, Conditional Factor DemandsUseful Diagrams:Consumer Thoery:SlutskyMatrix∂⎡∂∂⎡∂∂∂∂(Ordinal)Utility Maximization Expenditure Minimization (,)max ()x Marshallian Demand Function (,)(,):xiV p m U x p mx p m V p m =⋅=(,)min x st ()(,)e p u p U x ue p u =⋅>∂Monotonic Transformations 111221*********212212222(,)(,):(,)(,)(,)(,)(,)(,)(,)(,)(,)(,)Matrix Symmetry e p u e p u p p p p is Neg SemiDef e p u e p u p p p p h p u h p u e p u e p u p p p p p p e p u e p u h p u h p u p p p p p p ∂⎤⎢⎥∂∂∂∂⎢⎥∂∂⎢⎥⎢⎥∂∂∂∂⎣⎦∂∂⎤⎢⎥∂∂∂∂∂∂⎢⎥=∂∂∂∂⎢⎥⎢⎥∂∂∂∂∂∂⎣⎦11112(,)(,)(,)0,h p u h p u h p u p p p ⎡⎤⎢⎥∂⎢⎥→≤=⎢⎥∂⎢⎥⎣⎦2,)(,,im q q m μ)m=Producer Thoery:Conditional Demand Function Y=f(x)Profit MaximizationWe can do something similar to WAPM here. Notice that for a firm to Cost MinimizationProfit Function (,)max ()Input Demand Function (,)Supply Function (,)x p w pf x wx x p w y p w π=−Cost Function c(,)min :()(,)x w y wx SubjectTo f x yx w y ==y max (,)Solve py c w y −y profit maximize (p,w)= max (,).Since for any p,w we know y and (p,w), we can reconstruct c(w,y) from the points.py c w y ππ−。
MIT英文版线性代数试卷(1)
has
many solutions .
(b) What is the column space of A? Describe the nullspace of A.
Solution:
The column space is a 3-dimensional space inside a 3-dimensional space , i.e.
18.06 Linear Algebra
Spring 2010
For information about citing these materials or our Terms of Use, visit: /terms.
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MIT OpenCourseWare
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21年考研真题英语答案
21年考研真题英语答案来自21年考研真题的英语部分，本文将提供详细的答案解析以帮助考生更好地理解和准备考试。
以下将按照题目的顺序给出解答，并提供相关的解题思路和对答案的详细解析。
阅读理解部分：Passage 1:1. A解析：根据第一段的句子"Physicists have identified the source of "tricritical” magnetic behavior in a material that could benefit next-generation computing." 可知，物理学家已经找到了下一代计算机中受益的材料的“三重临界”磁性行为的来源。
根据上下文也可以判断出这是一项新的发现。
2. C解析：根据第三段 "This is the first time that a new type of magnetic behavior has been predicted theoretically and then discovered experimentally." 可知，从理论上预测然后通过实验证明这种新型磁性行为是第一次。
所以选C。
3. B解析：根据第六段 "These are intriguing discoveries that will help unlock novel electric and magnetic effects." 可知，这些都是令人感兴趣的发现，将有助于揭示新的电磁效应。
4. D解析：根据最后一段的最后一句 "The effort could also create a path to finding other novel materials with potentially useful properties." 可知，此举还可以为发现其他具有潜在有用性能的新材料铺平道路。
MIT量子物理exam
i A.Physical Constants and Conversion Factors Quantity Symbol Value UnitsAtomic mass unit amu931.5MeV/c21.661×10−27kgElectron mass m e0.511MeV/c29.109×10−31kgElementary charge e1.602×10−19C4.803×10−10esuPlanck’s constant h4.136×10−15eV s6.626×10−27erg s¯h=h/(2π)6.583×10−16eV s1.054×10−27erg sSpeed of light in vacuum c2.998×1010cm/s1eV=1.602×10−12erg1˚A=10−8cmhc=1.240×104eV˚A¯h c=1.973×103eV˚AB.Selected FormulaeEinstein-Planck relation:E=hν(1)DeBroglie relation:λ=hp(2)Rutherford scattering formula:dσdΩ=qQ2mv2◦21sin4(θ/2)(3)Radius of allowed orbits in Bohr model of hydrogenic atom:r n=n2Za0(4)wherea0=¯h2e2m(Bohr radius)(5)Solid angle of thin ring of width dθat angleθ(polar coordinates):dΩ=2πsinθdθ(6)11.Short Problems.(30points)(a).Davisson-Germer experiment(6points)A beam of electrons with kinetic energy K is scattered from a sin-gle crystal of nickel.A peak is observed in the diffraction pattern which is consistent with Bragg scattering of particles with wavelength λ=2.0˚A.What is the kinetic energy K(in units of eV)of the incident electrons?(b).Rutherford scattering(7points).In the Rutherford scattering ex-periment,a beam ofα-particles impinges upon a thin gold foil.Sig-nificant scattering is observed at large angles(some particles are even backscattered atθ=180◦).Find the ratio of the rate of particles that scatter into a thin ring of thickness dθatθ=100◦to those that scatter into a thin ring of thickness dθatθ=50◦.(c).Photoelectric effect(7points).As a result of shining monochromaticlight with wavelength800˚A on a metal surface,electrons are ejected which have a maximum kinetic energy of2eV.What is the maximum wavelength of light that can eject electrons from this metal surface?Compute the numerical value of this wavelength in angstroms(˚A).(d).Muonic atom(10points).The negative muon is a particle with thesame charge as the electron but with a larger mass(m=207m e).It is possible for the muon to be captured into orbits around the nuclei of atoms in a material and form a“muonic atom.”The inner orbit of the muon lies much closer to the nucleus than that of any electron.(i)(5points)Suppose the muon orbits a copper nucleus(Z=29).Find the radius of the innermost muonic orbit.Express your an-swer in units of a0(the Bohr radius for hydrogen).(ii)(5points)For copper,the energy of the n=2→n=1muonic transition is measured to be significantly lower than one wouldcalculate for a point nucleus.Explain briefly what this indicatesabout the radius of the copper nucleus.22.Bohr model for power law potential(30points)A particle of mass m moves in a central potential given byV(r)=V0 rak.(a).(16points)Use the Bohr quantization condition for angular momen-tum,L=n¯h,to calculate the quantized energies of allowed orbits of the particle.(Your answer should show the dependence on the quantum number n).(b).(7points)What value of k corresponds to the hydrogen atom?Findvalues for V0and a(or a suitable combination of these constants)which give the correct potential for hydrogen.(c).(7points)Use your result from parts a)and b)to calculate the energylevels of the hydrogen atom.33.Heisenberg Uncertainty Principle(20points)(a).(10points)A collimated stream of particles of mass m and charge qare accelerated from rest through a voltage V.They fall upon a slit of width d.What is the approximate angular divergence of the beam emerging from the other side?(b).(10points)Monochromatic light with wavelength of6000˚A passesthrough a fast shutter that opens for10−9sec.What is the approximate spread of wavelengths∆λof the light after it has passed through the shutter?4 4.Square wave function.(20points)The state of a free particle at t=0is described by the following wavefunction:Ψ(x,0)=⎧⎪⎨⎪⎩0x<−bA−b≤x≤3b 0x>3b.(a).(5points)Find A using the normalization condition.(You may choosethe phase convention such that A is real.)(b).(5points)What is the probability offinding the particle within theinterval x∈[0,b]at time t=0?(c).(10points)Calculate x and x2 for this state.。
2021年研究生英语模拟试卷与答案解析1
A：capacity
B：capability
C：ability
D：faculty
【答案】：A
【解析】：capacity指生产能力或容纳能力。B.capability用于人指智力方面的潜在能力，用于物指可能性或适应性；C.ability指人可通过学习来获得做好事的能力；D.faculty指人在某方面的特殊能力。
A：favorable to
B：interested in
C：hostile to
D：conscious of
【答案】：C
【解析】：词组辨析题。A.favorable to赞成;B.interested in对……感兴趣;C.hostile to敌对;D.conscious of意识到。本题上文出现大量负面词汇,如fear,reduce等。本句没有出现任何转折词汇,说明本句与上文关系为并列或递进,故该空也应填人负面词汇,从而使上下文正负色彩一致。选项中A.为正向词汇,B.D.偏向中性,唯有C.为负面词汇,故C.为答案。
2021年研究生英语模拟试卷与答案解析1
一、单选题(共40题)
1.Most of us have experienced the odd feeling of deja vu,often regarded as a supernatural force or a glitch in the matrix.You may perform an action and suddenly feel as though you have done it in that exact l manner sometime in your life.The feeling may even be 2 by a place or by spoken words,leaving some with the feeling they could 3 0r predict what happens next.Deja vu usually strikes without 4.But researchers from Colorado State University（CSU）have developed a technique to induce thes,6 previous experiment methods.Participants were led through virtual reality scenes 7 a junkyard or a hedge garden,which shared slight spatial similarities 8 were thematically unrelated.9 they could not"consciously remember the prior scene,"one researcher said,the participants'brain picked up on it and recognized"the similarity."The results showed deja vu"did not 10 above-chance ability to predict the next turn in a navigational path resembling a（n）11 experienced but unrecalled path,"although participants did report"12 feelings of knowing the direction of the next turn."Researchers 13 dejavu does not predict the future but makes people believe they can.It has been 14 as a"metamemory"phenomena,reflectinga（n）15 awareness of unspecific memories.Follow-up experiments are now being 16 by the team to look（）the main cause behind the feeling of prediction.The studies hope to address 18 it's the familiarity process that 19 the feeling,or hindsight bias 20 people feel convinced they knew what was going to happen after it happens
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麻省理工学院
电气工程与计算机科学系
6.302 反馈系统
2002下学期 开始日期：2002.11.4 实验2 截止时间：2002.11.21 星期四
引言
本实验的目的是给你增加一些动态系统补偿的经验。
在实验预习练习中，你已经通过分析，确定了三种合适的补偿策略：减小增益补偿，相位滞后补偿和相位超前补偿。
在本实验中，你将检验这些补偿策略是否能与预计的一样工作。
该过程和在讲课中看到的相似，实验参考资料请参阅Roberge的《运算放大器》的第177-191页。
我们已经改变了编号，用反相结构代替了正相结构，但原理是一样的。
器材
在器材桌上，确定已准备好以下器件：实验2元器件用具包，EZ带钩导线，十进电容器和一些连接线。
还需要一些在实验预习中根据各种补偿方案所计算出的元件。
伪运算放大器
实验系统将是下面的运算放大器，它具有与大家熟知和重复性好的运算放大器十分相似的
特性。
伪运算放大器的电路描述如图1所示。
23图1：运算放大器
你的第一步工作是搭建该运算放你大器电路，确信使用一片LM301A （而不是一片741）作为运算放大器，301A与741有相同的管脚输出（参看实验室墙壁上的图）；不要忘记给运算放大器的管脚7加+15V电源，给管脚4加-15V电源。
对于301A输出端的RC网络，使用元器件用具包中的精密元件（1%精度的电阻和5%精度的电容），使用短导线连接的十进电容器构成标称为C的电容
器；你可在该实验的标准化部分来调整它的值。
使用圆板电容器（F μ01.0）来解除±15V电源间的耦合－把他们连接在（1）+15V和地，（2）-15V和地之间；我们可以用图2所示的符号来表示运算放大器。
V +
V −
()A s out
V
图2：运算放大器符号
在本次实验的整个过程中，将会要求你在许多电路中使用运算放大器。
必须在所有的实验中使用同一个运算放大器。
就是说，如果要用两种方式补偿运算放大器，不用搭建两个独立的运算放大电路。
也要小心不要将电路中运算放大器烧坏。
如果301A的管脚1，5，8和任何可能的地方短路，包括地，会使它的性能变的非常差（通常失效）。
如果你弄坏了一个已经标准化过的放大器，你将不得不重新开始这个实验。
标准化
在该实验的所有部分中，运算放大器将被用来构成反相放大器，如图3所示。
f
R
图3：用运算放大器构成基本反相放大器
如果我们假设301A的传递函数由一个低频极点τ/1−=s 所决定，其中τ>> 10
3−秒，则开环传递函数有如下的形式： )110)(110)(1()()(4300+++=
−−s s s f a s f s A τ 其中， f
i i R R R f +=0
另外两个在103和104
rps处的极点与RC网络，包括与301A的输出阻抗有关。
不必惊讶，我
们注意到开环传递函数由运算放大器的两个特性决定（直流增益0a 和低频极点的位置τ/1−）。
因此，根据你所搭建的特殊电路特性不同，开环传递函数通常会有少许变化。
为了获得和你在实验预习中的分析计算相吻合的实验结果，需要对你搭建的运算放大电路进行标准化。
由于我们主要关心实验中系统的补偿结果和稳定程度，因此标准化就是在预期的穿越频率附近，使运算放大器的特性表示为一个已知的函数。
在a 0和τ两个参数中，我们不能控制0a ，但是通过调整十进电容器改变补偿电容C的值（301A管脚1和8之间的电容），可以完全控制τ的值。
通过下面的过程可以对运算放大器电路进行标准化：
1、搭建如图3所示的反相放大器电路，使k R i 62=，k R f 220=，使用1%精度的电阻。
2、实验中信号源的阻抗必须较低。
建议使用分压器对信号发生器的输出进行分压，并将该输出直接与运算放大器连接。
参考分压器电路如图4所示。
注意分压器的输出（到电路）连接放大器的输入（Vin）。
10K
图4 分压电路
3．给分压器施加一个低频小幅值的方波。
如果Vin的峰峰值（分压器的输出）超过50mv，用来进行线性分析的希望值将会严重失真。
(在大多数情况下，不准确的实验结果可能由这种错误引起)。
4.调整补偿电容C的值（十进电容器），使电路处于不稳定的临界状态。
阶跃响应“振铃”时间越长，极点离虚轴越近。
记录约10秒的振铃时间，但一般0.2秒到0.5秒就足够了。
C的取值范围大致是pF 5000左右。
确定该电路是振铃而不是发散振荡。
注意，在实验预习中通过分析确定τ值，从而获得零相位裕量系统的过程和这个实验过程是等价的。
在余下的实验中不要改变补偿电容的值
初始测量
现在，将阻值为的62k的电阻替换为阻值为22k的电阻，可将标准化过的运算放大器电路设置为增益为10的反相放大器。
又，应当使用精度为1％的精密电阻。
该电路将成为基本的未补偿
系统，在实验预习中的已计算了其特性。
其电路描述如图5所示。
图5 未补偿系统（增益为10的反相放大器）
测量该放大器的时域和频域响应（阻尼自然频率d ω，峰值时间p t ，超调量P.O.；谐振峰值幅度p M 以及谐振频率p ω）。
推导等效阻尼比和自然频率，并将这些值和实验预习中的计算值相比较。
补偿
现在可以通过下列方式补偿系统以改善系统的相位裕量：
1、 减少直流开环增益；
2、滞后补偿
3、超前补偿
你不要改变补偿电容C的值或运算放大器中RC网络的元件值，或使用不合理的网络实施补偿。
每个已补偿系统的电路图在实验预习中已给出，你应当使用在实验预习计算出的元件值0R （减小增益补偿），lag R 和lag C （滞后补偿），0R 和lead C （超前补偿）。
对每个已补偿系统进行时域和频域的测量，推导出阻尼比，自然频率和相位裕量。
还应该测量每个系统的带宽。
自己确认一下你测量的阶跃和频率响应是否与你在实验预习中的设计在一定程度上相一致。
实验报告
实验报告应当包含下列内容：
1、实验预习，包括方块图，伯德图，根轨迹，闭环零点和极点位置，补偿和未补偿系统的预期响应。
2、实现每个补偿器所用到的元件参数值。
3、每个补偿器测量的响应和计算出的闭环参数（n ωζ，和b ω）。
4、讨论每个补偿器的优缺点（比如直流增益，带宽，瞬态特性等）。