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Unformatted text preview: Your Name: T&AM 203 Final Exam Tuesday Dec 12, 2000 3:00 5:30 PM Draft March 20, 2007 5 problems, 100 points, and 150 minutes. Please follow these directions to ease grading and to maximize your score. a) No calculators, books or notes allowed. Ask for extra scrap paper if you need it. b) Full credit if free body diagrams are drawn whenever linear or angular momentum balance is used; correct vector notation is used, when appropriate; any dimensions, coordinates, variables and base vectors that you add are clearly defined; all signs and directions are well defined with sketches and/or words;  reasonable justification, enough to distinguish an informed answer from a guess, is given; you clearly state any reasonable assumptions if a problem seems poorly defined poorly defined ; work is I. ) neat, II. ) clear, and III.) well organized; your answers are TIDILY REDUCED (Dont leave simplifiable algebraic expressions.); your answers are boxed in; and unless otherwise stated, you will get full credit for, instead of doing a calculation, presenting Matlab code that would generate the desired answer. To ease grading and save space, your Matlab code can use shortcut notation like 7 = 18 instead of, say, theta7dot = 18 . Pick generic (not special) numerical values for constants not defined in the problem statement. c) Substantial partial credit if your answer is in terms of well defined variables and you have not substi tuted in the numerical values. Substantial partial credit if you reduce the problem to a clearly defined set of equations to solve. Problem 1: /20 Problem 2: /20 Problem 3: /20 Problem 4: /20 Problem 5: /20 TOTAL: /100 1)(20 pts) Spring mass. a) (5 pts) Find the equation of motion, a differential equation, for the variable x in the system above. Your differential equation can contain x , its time derivatives, m, c, k, and (Please read item (b) on the cover page.) b) (5 pts) Assume c = 0, x ( t = 0) = d , and x ( t = 0) = 0. What is x at time t (answer in terms of some or all of m, k, , d, and t . c) (5 pts) Assume relatively large c ( c 2 > 4 km ), x ( t = 0) = d , and x ( t = 0) = 0. Find x ( t ) (or write code that would find x ( t )). d) (5 pts) Whether or not you have succeeded at part (c) above, make a clear plot of x vs t for the conditions in part (c) above. (work for problem 1, contd.) 2)(20 pts) Car on a ramp. A junior level engineering design course asks students to build a cart (mass = m c ) that rolls down a ramp with angle . A small weight (mass m w m c ) is placed on top of the cart on a surface tipped with respect to the cart (angle...
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This note was uploaded on 07/09/2009 for the course ENGRD 2030 taught by Professor Ruina during the Spring '08 term at Cornell University (Engineering School).
 Spring '08
 RUINA

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