MIT 3 016 - Mathematical Methods for Materials Scientists and Engineers

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Massachusetts Institute of TechnologyMathematical Methodsfor Materials Scientists and Engineers3.016 Fall 2005W. Craig CarterDepartment of Materials Science and EngineeringMassachusetts Institute of Technology77 Massachusetts Ave.Cambridge, MA 02139Problem Set 5: Due Wed. Nov. 30, Before 5PM: email to [email protected] following are t his week’s randomly assigned homework groups. The first member of thegroup is the “Homework Jefe” who will be in charge of setting up work meetings and have respon-sibility for turning in the group’s homework notebook. If some some reason, the first member inthe list is incapacitated, recalcitrant, or otherwise unavailable, then the second member shouldtake that position. Attention slackers: The Jefe should include a line at the top of your notebooklisting the group members that participated in the notebook’s production. Group names are bold-faced text.Accio: Jason Pelligrino (jpell19),Lauren Oldja (oldja), Richard Ramsaran (rickyr21), Jill Rowehl(jillar), JinSuk Kim (jkim123)Colloportus: John Pavlish (jpavlish), Leanne Veldhuis (lveldhui), Jina Kim (jinakim), SamuelSeong (sseong), Annika Larsson (alarsson)Densaugeo: Maricel Delgadillo(maricela), Allison Kunz (akunz), Kyle Yazzie (keyazzie), SaahilMehra (smehra), Vladimir Tarasov (vtarasov)Rictusempra: Eugene Settoon (geneset),EunRae Oh (eunraeoh), Kimberly Kam (kimkam), CharlesCantrell (cantrell), Omar Fabian (ofabian)Riddikulus: John Rogosic (jrogosic),Kelsey Vandermeulen (kvander), Rene Chen (rrchen), MicheleDufalla (mdufalla), Talia Gershon (tgershon)Scourgify: Bryan Gortikov (bryho),Emily Gullotti (emgull), Lisa Witmer (witmer), KatrineSivertsen (katsiv), Katherine Hartman (khartman)1Individual Exercise I5-1Kreyszig MathematicarComputer Guide: problem 9.4, page 107Individual Exercise I5-2Kreyszig MathematicarComputer Guide: problem 9.12, page 108Individual Exercise I5-3Kreyszig MathematicarComputer Guide: problem 9.18, page 109Individual Exercise I5-4Kreyszig MathematicarComputer Guide: problem 9.20, page 109Individual Exercise I5-5Kreyszig MathematicarComputer Guide: problem 10.4, page 120Individual Exercise I5-6Kreyszig MathematicarComputer Guide: problem 10.14, page 120Individual Exercise I5-7Kreyszig MathematicarComputer Guide: problem 11.8, page 131Individual Exercise I5-8Kreyszig MathematicarComputer Guide: problem 1.18, page 15Individual Exercise I5-9Kreyszig MathematicarComputer Guide: problem 2.2, page 28Individual Exercise I5-10Kreyszig MathematicarComputer Guide: problem 2.16, page 302Group Exercise G5-1Consider an infinite sheet o f thickness a and a thin disk of radius R and thickness b which interactthrough the London interaction.1. Upon how many different variables does the interaction energy depend?2. By rescaling variables, re-express the interaction energy in terms of dimensionless units.3. Can you calculate the form of the London interaction? between an an infinite sheet ofthickness a and a thin disk of radius R and thickness b?4. Use graphics to visualize the results of your calculations.Group Exercise G5-2Download the data from http://www-personal.buseco.monash.edu.au/˜hyndman/TSDL/ (SOI.DAT)that describes the monthly difference in in sea-surface air pressure between Darwin, Australia andTa hiti during Jan 1882—May 1 993. There is some missing data in this set.1. Plot the data as a f r action of the standard deviation versus time.2. Fit the data with a linear model (i.e., y = y0+mx). Plot and discuss the model’s applicability.3. Create a new da ta set by subtracting the linear model from the original data. Interpret themeaning of this new data set.4. To analyze whether there may be any monthly, bi-monthly, or seasonal trends, fit your datawith a trigonometric or Fourier series. Comment on the a ppearance of any trends.5. Use your models to provide estimates of the missing data.6. Predict the pressure difference between Darwin and Ta hiti in the year 2 006.Group Exercise G5-3At the MIT Z-Center 3 meter diving board, an average student standing at the end of the divingboard causes a deflection of about 0.4 meters.1. If the diving board is 4 meters long, estimate the product of the elastic modulus and momentof inertia, EI, for the diving board. Estimate the Young’s modulus of the diving boardmaterial. Track down a an experimental value for wood’s elastic moduli and use this datato compare to your estimate.2. Create an animation of the diving board deflection as an average student walks from oneend of this diving board to another.3. Create an animation of the diving board deflection as average students crawls on his/herstomach to the end of t he diving board.4. Create an animation as a gro up of r andom students each holding the hand of the studentbehind them, walk onto the diving boar


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