2007midterm

2007midterm - MS&E201 Dynamic Systems Spring 2007...

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MS&E201 Dynamic Systems Page 1 of 14 Spring 2007 May 9, 2007 Professor Edison Tse MS&E 201 DYNAMIC SYSTEMS MIDTERM EXAM 75 minutes, total 100 points Open Book. Open Notes. No computers are permitted at the examination. Calculations will be kept as simple as possible, and you will receive most of the credit for setting up calculations correctly, even if you do not carry them out. Partial credit will be given whenever possible, provided your solution is neat and clear. Please underline your final answers for each question Off-campus SCPD students: please write down the start and finish time of your midterm. . The Honor Code Applies: “On my honor, I have neither given nor received unauthorized assistance on this examination, and I have abided by all other provisions of the honor code in taking this examination.” Signature: __________________________________ Printed Name: __________________________________ Please do not open the examination until you are asked to begin. Please check to ensure that your exam contains 14 pages (including cover sheet) with 4 questions. Total Score: / 100 + / 10 (Bonus: Attempt only when you have finished the other questions)
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MS&E201 Dynamic Systems Page 2 of 14 Spring 2007 May 9, 2007 Professor Edison Tse Problem 1. Short Answer Questions [25 points] You should explain your answer briefly to get full credit During class we introduced a few basic models that you can use to model a dynamic system. What would be the most appropriate model for the following systems? Why? The fate of the Universe (6 points) Almost all scientists agree on the fact that the Universe began from the Big Bang, but its fate is still uncertain. In fact, galaxies and clusters are subject to two forces that counter- act since the Universe began: the gravitational attraction force, which would tend to make the Universe collapse upon itself, and the expansion push of the Big Bang. Which will win? It is hard to say: it depends on how much mass the Universe exactly contains. The astronomers found a critical density of the Universe, equal to about 10 - 30 grams per cubic centimeter, and so a critical mass, for which the two forces would exactly balance. If the mass of the Universe is larger than the critical mass, the gravitational force will someday prevail. The expansion will slow down until stopping, and slowly the Universe will start contracting under the effect of its own gravitation. Galaxies will get closer until they will merge, and stars will, too. The entire Universe, composed with
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2007midterm - MS&E201 Dynamic Systems Spring 2007...

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