MAT2705-03/04 11F Final Exam Print Name (Last, First) _________________________________|__
Show all work, including mental steps, in a clearly organized way that speaks for itself. Use proper mathematical notation, identifying expressions by their proper symbols (introducing them if necessary), and use arrows and equal signs when appropriate. Always simplify expressions. BOX final short answers. LABEL parts of problem. Keep answers EXACT (but give decimal approximations for interpretation). Indicate where technology is used and what type (Maple, GC), REALLY. You are encouraged to use technology to check all of your hand results.
A certain physical system has the following equations of motion and initial conditions:
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 where 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, 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, 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a) Rewrite this system of DEs and its initial conditions as 6 scalar equations. Solve this system with Maple and write down the solutions for the two unknowns.b) By hand showing all steps, find the smallest integer component eigenvectors 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 of the coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= produced by the solution algorithm after rescaling of the standard results by positive multiples if necessary, ordered so that the corresponding eigenvalues satisfy 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. Evaluate the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYjUSFGJy9GM1Enbm9ybWFsRic= =LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSVtc3ViR0YkNiUtRiM2KS1JI21pR0YkNiNRIUYnLUYjNiVGNS1JJm1vdmVyR0YkNiUtRjY2J1EiYkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGQy8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSSNtb0dGJDYuUS0mUmlnaHRBcnJvdztGJy8lLHBsYWNlaG9sZGVyR0ZDL0ZHUSdub3JtYWxGJy8lJmZlbmNlR1EmdW5zZXRGJy8lKnNlcGFyYXRvckdGVi8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZWLyUobGFyZ2VvcEdGVi8lLm1vdmFibGVsaW1pdHNHRlYvJSdhY2NlbnRHRlYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0Zfby9GXG9GQ0ZSRjVGQUZERkZGSS1GIzYkLUkjbW5HRiQ2JFEiMUYnRlJGUi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUZNNi1RInxnckYnRlIvRlVRJmZhbHNlRicvRlhGYHBGWS9GZm5GYHAvRmhuRmBwL0ZqbkZgcC9GXG9GYHAvRl5vUSwwLjExMTExMTFlbUYnL0Zhb0ZncC1GMTYlRjMtRiM2JC1GZm82JFEiMkYnRlJGUkZpb0ZSRlIvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnRlI= and its inverse, and the diagonalized matrix 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. [Use technology to check that your inverse is correct.]c) What are the slopes 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 of the lines through the origin containing the two eigenvectors? On the grid provided, draw in those two lines, labeling them by their corresponding coordinates 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 in the positive direction determined by the eigenvectors and then indicate by thicker arrows both eigenvectors 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 , labeled by their symbols. Recall LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkmbW92ZXJHRiQ2JS1GIzYnLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGNi8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGNEY3RjlGPC1JI21vR0YkNi5RLSZSaWdodEFycm93O0YnLyUscGxhY2Vob2xkZXJHRjYvRjpRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRjYvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlgvRlVGNi1GQDYvUSI9RidGNC9GOkY+RjxGR0ZKL0ZNRklGTkZQRlJGVEZWRlktRjE2JVEiQkYnRjcvRjpRJ2l0YWxpY0YnLUZANi9RIn5GJ0Y0RmluRjxGR0ZKRmpuRk5GUEZSRlQvRldRJjAuMGVtRicvRlpGZG8tRiw2JS1GMTYnUSJ5RidGNEY3RjlGPEY/RmVuLUZANi1RIixGJ0ZFRkcvRktGNkZqbkZORlBGUkZURmNvL0ZaUSwwLjMzMzMzMzNlbUYnLUZANi1GYm9GRUZHRkpGam5GTkZQRlJGVEZjb0Zlb0Zmby1GQDYtRmhuRkVGR0ZKRmpuRk5GUEZSRlRGVkZZLUklbXN1cEdGJDYlRltvLUYjNiYtRkA2LVEqJnVtaW51czA7RidGRUZHRkpGam5GTkZQRlJGVC9GV1EsMC4yMjIyMjIyZW1GJy9GWkZecS1JI21uR0YkNiRRIjFGJ0ZFRjdGXm8vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRmFwRistRjE2I1EhRidGRQ==, where 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. Also label the 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 axes.
d) Find by hand the general solution of the corresponding decoupled system of DEs 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 .First write them out in matrix form, then obtain the two equivalent scalar DEs which are its components. Then solve them to find their general solutions using the method of undetermined coefficients, identifying the homogeneous and particular parts of each solution: 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. State your solution in scalar form and box it: 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 .e) Then express the general solution for 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 and impose the initial conditions. Write out and box the scalar solutions: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ0RidGMkY1Rj5GPi1JI21vR0YkNi1RIj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZRLyUpc3RyZXRjaHlHRlEvJSpzeW1tZXRyaWNHRlEvJShsYXJnZW9wR0ZRLyUubW92YWJsZWxpbWl0c0dGUS8lJ2FjY2VudEdGUS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmpuLUZMNi1RIy4uRidGPkZPRlJGVEZWRlhGWkZmbi9GaW5RLDAuMjIyMjIyMmVtRicvRlxvUSYwLjBlbUYnLUZMNi1RIi5GJ0Y+Rk9GUkZURlZGWEZaRmZuL0ZpbkZjb0Ziby1GTDYtUSIsRidGPkZPL0ZTRjRGVEZWRlhGWkZmbkZnby9GXG9RLDAuMzMzMzMzM2VtRictRiw2JUYuLUYjNiQtRjs2JFEiMkYnRj5GPkZARkNGS0Zdb0Zkby1GTDYtUSJ+RidGPkZPRlJGVEZWRlhGWkZmbkZnb0Zib0Y+. Do they agree with Maple's solution? If not, look for your error. Did you input the equations correctly?f) Express your (correct) solution as a sum of the two eigenvector modes and the response mode in the form: 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 thus identifying the particular solution 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 (last term), the response vector coefficient 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 and the homogeneous solution 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 (first two terms). What are the values of the natural frequencies LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y1 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1 associated with the homogeneous solution? Which frequency is associated with the tandem mode (same signed eigenvector components) and which with the accordian mode (opposite signed eigenvector components)?
g) On the grid provided, draw in the vector 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. What are its new coordinates 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? On your graph, draw in the parallelogram parallel to the new coordinate axes which projects this vector along those axes and identify the sides of the parallelogram on those axes by the number of multiples of the corresponding eigenvector, i.e., 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 and 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. Do these seem consistent with your plot?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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEtRWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEiQUYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZARj1GQA==Re-order eigenvalues and eigenvectors so 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LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYlKiRJIkJHRighIiItJkknVmVjdG9yR0YqNiNJJ2NvbHVtbkdGKDYjL0kkJWlkR0YoIiorbXgrJkkldHJ1ZUdGJQ==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Equating top and bottom lines gives the scalar DEs, to which we add the scalar components of the initial conditions: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 is the grid:LUkoZGlzcGxheUc2IjYkLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYoIiIhOyEjNSIjNUYtL0kmY29sb3JHRiRJJmJsYWNrR0YkL0kqdGhpY2tuZXNzR0YkIiIjL0klYXhpc0dGJDcjL0kqZ3JpZGxpbmVzR0YkNyUiI0AvRjQiIiJGMC1GJzYlNyQ3JEYsRi43JEYsRi9GM0YwJSFHpledgeWhen you have completed the exam, please read and sign the dr bob integrity pledge and hand this test sheet stapled on top of your answer sheets as a cover page, with the first test page facing up:"During this examination, all work has been my own. I have not accessed any of the class web pages or any other sites during the exam. I give my word that I have not resorted to any ethically questionable means of improving my grade or anyone else's on this examination and that I have not discussed this exam with anyone other than my instructor, nor will I until after the exam period is terminated for all participants."
Signature: Date: 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TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ0NjM0NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyYlIm1HNiQiIiJGKSZGJzYkIiIjRilGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ1MzQ0NzY2NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyIiJSIiIkYl