MAT2705-02/06 10F 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 coupled pair of oscillators has the following equations of motion and initial conditions:
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 .
a) Rewrite this system of DEs and its initial conditions in explicit matrix form for the (column matrix) vector variable 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 , identifying the coefficient matrix A.
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, ordered so that the corresponding eigenvalues satisfy 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. Evaluate the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYjUSFGJy9GM1Enbm9ybWFsRic= =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 and its inverse. [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 NiQmSVEjbW92ZXIobWkoImIiLGZvbnR3ZWlnaHR+PX4iYm9sZCIpLG1vKCImcmFycjsiKSlHNiI2IyIiIiZGJDYjIiIj , labeled by their symbols. Recall 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, where 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. Also label the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIsRidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlRi4tRiM2JC1GOzYkUSIyRidGPkY+RkAtRi82I1EhRidGPg== axes.
d) Now by hand solve the initial value problem stated above before part a). First write out the new decoupled equations LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 first in vector form, then the two equivalent scalar equations. Then solve them to find their general solution. State it and box it: 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 .Then express the general solution for LUkmbW92ZXJHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JS1JI21pR0YkNidRInhGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHRjEvJSxtYXRodmFyaWFudEdRLGJvbGQtaXRhbGljRicvJStmb250d2VpZ2h0R1ElYm9sZEYnLUkjbW9HRiQ2LlEtJlJpZ2h0QXJyb3c7RicvJSxwbGFjZWhvbGRlckdGMS9GNVEnbm9ybWFsRicvJSZmZW5jZUdRJnVuc2V0RicvJSpzZXBhcmF0b3JHRkQvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGRC8lKGxhcmdlb3BHRkQvJS5tb3ZhYmxlbGltaXRzR0ZELyUnYWNjZW50R0ZELyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUy9GUEYx and impose the initial conditions. Write out the scalar solution: 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. Does it agree with Maple's solution? If not, write down Maple's solution and look for your error. Did you input the equations correctly?
e) 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 (last term), the response vector coefficient 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 and the homogeneous solution 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 (first two terms). Also write down your solutions 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 .
f) 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?g) Evaluate the amplitudes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJBRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIxRicvRjtRJ25vcm1hbEYnRjdGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEiLEYnRkMvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGTi8lKnN5bW1ldHJpY0dGTi8lKGxhcmdlb3BHRk4vJS5tb3ZhYmxlbGltaXRzR0ZOLyUnYWNjZW50R0ZOLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JUYzLUYjNiUtRkA2JFEiMkYnRkNGN0Y6RkVGQ0ZDRkM= and phase shifts 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 of 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 and 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. Make sure each computation is accompanied by a diagram showing the appropriate quadrant needed to get the phase shift angle correct. Give their exact values and their numerical values, with the phase shift numerical values in degrees to the nearest degree.solutiona)
I am lazy. Instead of typing the function notation "(t)" after every unknown in the deqs, I set the independent differentiation variable to be LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Here is the system of deqs: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PkkiZkc2Ii1JJDwsPkdJKF9zeXNsaWJHRiQ2JCIiISwkLUkkc2luRzYkJSpwcm90ZWN0ZWRHRic2IywkSSJ0R0YkIiIkIiNxa)
The vector deqs areLy1JJDwsPkdJKF9zeXNsaWJHNiI2JC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSN4MUdGJjYjSSJ0R0YmRi9GLy1GKTYlLUkjeDJHRiZGLkYvRi8sJi1JMGRlbGF5RG90UHJvZHVjdEc2JEYqL0krbW9kdWxlbmFtZUdGJkksVHlwZXNldHRpbmdHNiRGKkYlNiVJIkFHRiYtRiQ2JEYsRjJJJXRydWVHRioiIiJJImZHRiZGQQ==and initial conditionsQyUvLUkkPCw+R0koX3N5c2xpYkc2IjYkLUkjeDFHRic2IyIiIS1JI3gyR0YnRistRiU2JEYsRiwiIiIvLUYlNiQtLUkiREc2JCUqcHJvdGVjdGVkR0YmNiNGKkYrLS1GNzYjRi5GK0Yvb)PjYkSSdMYW1iZGFHNiJJIkJHRiUtX0kuTGluZWFyQWxnZWJyYUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJUktRWlnZW52ZWN0b3JzR0YlNiMtSSdNYXRyaXhHRio2Iy9JJCVpZEdGJSIqN3FBUiI=Qys+SSNiMUc2IiwkLUknQ29sdW1uR0YlNiRJIkJHRiUiIiIiIiVGKz5JI2IyR0YlLCQtRig2JEYqIiIjRjJGKz5JI0JCR0YlLUkkPHxncj5HSShfc3lzbGliR0YlNiRGJEYuRisqJEY0ISIiRistSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YlSSxUeXBlc2V0dGluZ0c2JEY+Rjc2JS1GPDYlRjlJIkFHRiVJJXRydWVHRj5GNEZHPkkjZnlHNiItSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSSxUeXBlc2V0dGluZ0c2JEYoSShfc3lzbGliR0YkNiUqJEkjQkJHRiQhIiItSSQ8LD5HRi02JCIiISwkLUkkc2luR0YsNiMsJEkidEdGJCIiJCIjcUkldHJ1ZUdGKA==details:LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKld2enMiLV9JLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiJJLERldGVybWluYW50R0YoNiMtSSdNYXRyaXhHRiU2Iy9JJCVpZEdGKCIqV3Z6cyI=QyUtSSdmYWN0b3JHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kiJUdGKCIiIi1JJnNvbHZlR0YlRik=c)
The slopes of the lines through the origin containing the eigenvectors areQyUvJkkiTUc2IjYjIiIiIiIlRigvJkYlNiMiIiMsJC1JIi9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IyEiIkYtso the lines areNiQvJkkieEc2IjYjIiIjLCQmRiU2IyIiIiIiJS9GJCwkRiohIiM=e) mode identificationSSVYc29sRzYiPkkmWHNvbDJHNiIsKComLCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkSSJ0R0YkIiIjIiIiLUkkc2luR0YqRi0jIiIoRjBGMUkjYjFHRiRGMUYxKiYsJi1GKTYjLCRGLyIiJSEiIi1GM0Y6IyEiJkY8RjFJI2IyR0YkRjFGMSomLUYzNiMsJEYvIiIkRjEtSSQ8LD5HRiw2JEYwRkZGMSEiIw==c) solution steps:Ly1JJDwsPkdJKF9zeXNsaWJHNiI2JC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSN5MUdGJjYjSSJ0R0YmRi9GLy1GKTYlLUkjeTJHRiZGLkYvRi8sJi1JMGRlbGF5RG90UHJvZHVjdEc2JEYqL0krbW9kdWxlbmFtZUdGJkksVHlwZXNldHRpbmdHNiRGKkYlNiUtSSdNYXRyaXhHRjs2Iy9JJCVpZEdGJiIqVyNIJmYiLUYkNiRGLEYySSV0cnVlR0YqIiIiSSNmeUdGJkZGPkkmZGVxc3lHNiI2JC8sJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSN5MUdGJDYjSSJ0R0YkRi9GLyIiIkYsIiIlJkkjZnlHRiQ2I0YwLywmLUYpNiUtSSN5MkdGJEYuRi9GL0YwRjkiIzsmRjM2IyIiIw==particular solutions from method of undetermined coefficients:LUklZXZhbEclKnByb3RlY3RlZEc2Iy1JJXN1YnNHRiQ2JS8tSSN5MUc2IjYjSSJ0R0YsKiZJI2M1R0YsIiIiLUkkc2luRzYkRiRJKF9zeXNsaWJHRiw2IywkRi4iIiRGMS8tSSN5MkdGLEYtKiZJI2M2R0YsRjFGMkYxPCNJJmRlcXN5R0YsQyU+SSNDNUc2Ii1JJnNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvLCRJI2M1R0YlISImIyIjTiIiJCIiIj5JI0M2R0YlLUYnNiMvLCRJI2M2R0YlIiIoRjA=plus the homogeneous solutions from memory: 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:PkkoeXNvbGdlbkc2Ii1JJ2Rzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkPCNJJmRlcXN5R0YkPCQtSSN5MUdGJDYjSSJ0R0YkLUkjeTJHRiRGMA==back to the original variables:PkkoWHNvbGdlbkc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiRJKHlzb2xnZW5HRiQtSTBkZWxheURvdFByb2R1Y3RHNiRGJy9JK21vZHVsZW5hbWVHRiRJLFR5cGVzZXR0aW5nRzYkRidJKF9zeXNsaWJHRiQ2JUkjQkJHRiQtSSQ8LD5HRjE2JC1JI3kxR0YkNiNJInRHRiQtSSN5MkdGJEY5SSV0cnVlR0YnNow the initial conditionsQyUtSSVzdWJzRyUqcHJvdGVjdGVkRzYkL0kidEc2IiIiIUkoWHNvbGdlbkdGKSIiIi1JJnNvbHZlRzYkRiVJKF9zeXNsaWJHRik2JDwkLyZJIiVHRik2I0YsIiIjLyZGNTYjRjdGNzwkSSRfQzFHRilJJF9DM0dGKQ==QyUtSSlzaW1wbGlmeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLUklc3Vic0dGJjYkL0kidEdGKCIiIS1JJG1hcEdGJjYlSSVkaWZmR0YmSShYc29sZ2VuR0YoRi4iIiItSSZzb2x2ZUdGJTYkPCQmSSIlR0YoNiNGNSZGOzYjIiIjPCRJJF9DMkdGKEkkX0M0R0YoQyUtSSVzdWJzRyUqcHJvdGVjdGVkRzYkPCYvSSRfQzFHNiIhIiIvSSRfQzJHRiojISImIiIlL0kkX0MzR0YqIiIiL0kkX0M0R0YqIyIiKCIiI0koeXNvbGdlbkdGKkYzPkklWXNvbEdGKi1GJDYkSSIlR0YqLUkkPCw+R0koX3N5c2xpYkdGKjYkLUkjeTFHRio2I0kidEdGKi1JI3kyR0YqRkU=Qyk+SSNBMUc2Ii1JJXNxcnRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywmLUkiXkdGKTYkIiIiIiIjRjAtRi42JCMiIihGMUYxRjBGMC1JJmV2YWxmR0YpNiRJIiVHRiUiIiVGMD5JI0EyR0YlLUYnNiMsJi1GLjYkISIiRjFGMC1GLjYkIyEiJkY6RjFGMEYwRjY=Qy0+JkkmZGVsdGFHNiI2IyIiIi1JJ2FyY3Rhbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjIyIiKCIiI0YoLUkmZXZhbGZHRiw2IyomSSIlR0YmRigtSSIvR0YrNiMsJEkjUGlHRixGMUYoRigtRjM2IywkKiZGNkYoSShkZWdyZWVzR0YmRigiJGckRig+JkYlNiNGMSwmRjshIiItRio2IyMiIiYiIiVGKEYoRjJGKEY8LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYlKiRJI0JCR0YoISIiLUkkPCw+R0YrNiQiIiNGM0kldHJ1ZUdGJQ==Not requested: the frequencies and periods 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 common period is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGOEYvRi8=. The amplitude ratios LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSI6RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZYLUYsNiVGLi1GIzYkLUY7NiRRIjJGJ0Y+Rj5GQEY+ for the frequencies 2, 4, 3 are 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PkkiVEc2IiwkSSNQaUclKnByb3RlY3RlZEciIiM=JSFHQyQtSSVzdWJzRyUqcHJvdGVjdGVkRzYkSSRzb2xHNiI3JC1JI3gxR0YoNiNJInRHRigtSSN4MkdGKEYsISIiQyY+SSVwYXRoRzYiLUkjb3BHJSpwcm90ZWN0ZWRHNiNJIiVHRiUhIiItSSZldmFsZkdGKDYkSSMlJUdGJSIiJSIiIg==QyQtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiY3I0klcGF0aEdGKC9JInRHRig7IiIhSSJUR0YoL0kmY29sb3JHRig3JEkkcmVkR0YoSSVibHVlR0YoL0kqZ3JpZGxpbmVzR0YoSSV0cnVlR0YmIiIiQyktSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiU3JEklcGF0aEdGKC9JInRHRig7IiIhSSJUR0YoL0knbGFiZWxzR0YoNyRJI3gxR0YoSSN4MkdGKC9JKHNjYWxpbmdHRihJLGNvbnN0cmFpbmVkR0YoIiIiPkkncGN1cnZlR0YoSSIlR0YoISIiLy1JJDwsPkdGJzYkRjRGNS1JJXN1YnNHRiY2JEkkc29sR0YoLUZANiQtRjQ2I0YtLUY1RklGOS1JJmV2YWxmR0YmNiRGPCIiJA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=Now the plot.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 fun we look at the full solution curve superimposed on this diagram.QywtSSVwbG90RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiY3JCwkSSN4eEdGKCIiJSwkRiwhIiMvRiw7ISImIiImL0kmY29sb3JHRihJJmdyZWVuR0YoL0kqdGhpY2tuZXNzR0YoIiIiISIiPkkncGxpbmVzR0YoSSIlR0YoRjotSShkaXNwbGF5R0YoNipJI3A1R0YoRjxJI2EzR0YoSSNhNEdGKEkjYTFHRihJI2EyR0YoSSNhNUdGKC9JKmdyaWRsaW5lc0dGKEkldHJ1ZUdGJkY6PkkmcG5pY2VHRihGPUY6LUY/NiRGS0kncGN1cnZlR0YoRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoZGlzcGxheUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBuaWNlRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSdwY3VydmVGJ0YvRjJGQQ==Here is the grid:LUkoZGlzcGxheUc2IjYlLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkIiIhOyQhI2IhIiIkIiNiRjAvSSpncmlkbGluZXNHRiRJJXRydWVHRikvSSV2aWV3R0YkNyRGLUYtpledgeWhen 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: gridline default plot windowLUklcGxvdEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYlIiIhL0kldmlld0dGJzckOyQhI2IhIiIkIiNiRjBGLS9JKmdyaWRsaW5lc0dGJ0kldHJ1ZUdGJQ==The actual motion is pretty crazy due to the driving 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TTdSMApJNVJUQUJMRV9TQVZFLzUyNDI3Mjg0WColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiIyIjJSN4MUclI3gyR0YlTTdSMApJNVJUQUJMRV9TQVZFLzUyNDA5MzcyWColKWFueXRoaW5nRzYiRiVbZ2whIyUhISEiIyIjLCwtJSRzaW5HNiMsJCUidEciIiQhIiUtJSRjb3NHNiMsJEYrIiIjIiIiLUYvNiMsJEYrIiIlRjMtRihGMCMiIihGMi1GKEY1IyIiJkY3LCxGJyEiJ0YuRjdGNCEiI0Y4IiM5RjsjISImRjJGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzEzOTIyNzAxMlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyUiIyIjISM3IiM7IiIjISIpRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1NTQwMTYyNFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyIiISwkLSUkc2luRzYjLCQlInRHIiIkIiNxRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE3MTkwMjE5NlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIy0lJWRpZmZHNiQtRic2JC0lI3gxRzYjJSJ0R0YuRi4tRic2JC1GJzYkLSUjeDJHRi1GLkYuRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE3MTkwMjQ1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywmLSUjeDFHNiMlInRHISM3LSUjeDJHRikiIiMsKEYnIiM7RiwhIiktJSRzaW5HNiMsJEYqIiIkIiNxRiU=TTdSMApJNlJUQUJMRV9TQVZFLzEzOTI2MjU3NlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIy0lI3gxRzYjIiIhLSUjeDJHRihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzEzOTI2MjMyMFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyIiIUYmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzEzOTI2MjAzMlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIy0tJSJERzYjJSN4MUc2IyIiIS0tRig2IyUjeDJHRitGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzEzOTI2MTA0MFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyIiIUYmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1ODM4NDc4MFgqJSphbGdlYnJhaWNHNiJGJVtnbCEjJSEhISIjIiMhIiUhIztGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1ODM4NDcwMFgsJSphbGdlYnJhaWNHNiJGJVtnbCEiJSEhISMlIiMiIyMiIiIiIiVGJyMhIiIiIiNGJ0YlTTdSMApJNlJUQUJMRV9TQVZFLzE1ODM0NDQ3NlgqJSphbGdlYnJhaWNHNiJGJVtnbCEjJSEhISIjIiMiIiIiIiVGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1ODM0NDE1NlgqJSphbGdlYnJhaWNHNiJGJVtnbCEjJSEhISIjIiMhIiIiIiNGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1ODM0MDk1NlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyUiIyIjIiIiIiIlISIiIiIjRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1ODU0MDM4OFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyUiIyIjIyIiIiIiJCMhIiNGKCNGJyIiJ0YrRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1ODc3MDk4NFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyUiIyIjISIlIiIhRichIztGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1OTA1MjIwNFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywkLSUkc2luRzYjLCQlInRHIiIkIyIjTkYsRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE3Mjc5NzU0NFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhIyUiIyIjLCYhIzciIiIlJ2xhbWJkYUchIiIiIzsiIiMsJiEiKUYoRilGKkYlTTdSMApJNlJUQUJMRV9TQVZFLzE1ODM0NjkwOFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyUjeDFHJSN4MkdGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1ODM0NzAzNlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsLSUkc2luRzYjLCQlInRHIiIkISIlLSUkY29zRzYjLCRGKyIiIyIiIi1GLzYjLCRGKyIiJUYzLUYoRjAjIiIoRjItRihGNSMiIiZGNywsRichIidGLkY3RjQhIiNGOCIjOUY7IyEiJkYyRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1OTAxMDg5MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsLSUkc2luRzYjLCQlInRHIiIkISIlLSUkY29zRzYjLCRGKyIiIyIiIi1GLzYjLCRGKyIiJUYzLUYoRjAjIiIoRjItRihGNSMiIiZGNywsRichIidGLkY3RjQhIiNGOCIjOUY7IyEiJkYyRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1OTUyODczMlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIy0lJWRpZmZHNiQtRic2JC0lI3kxRzYjJSJ0R0YuRi4tRic2JC1GJzYkLSUjeTJHRi1GLkYuRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1OTk3MTI0OFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywmLSUjeTFHNiMlInRHISIlLSUkc2luRzYjLCRGKiIiJCMiI05GMCwmLSUjeTJHRikhIztGLEYxRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE2Mjg0MDU1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsKiYtJSRzaW5HNiMsJCUidEciIiMiIiIlJF9DNEdGLkYuKiYtJSRjb3NHRipGLiUkX0MzR0YuRi4tRik2IywkRiwiIiQhIiUqJi1GKTYjLCRGLCIiJUYuJSRfQzJHRi4hIiIqJi1GMkY7Ri4lJF9DMUdGLkY/LCxGJ0Y9RjBGPUY0ISInRjlGLUZARi1GJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE2Mjg0MDYxNlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsKiYtJSRzaW5HNiMiIiEiIiIlJF9DNEdGLEYsKiYtJSRjb3NHRipGLCUkX0MzR0YsRixGKCEiJSomRihGLCUkX0MyR0YsISIiKiZGL0YsJSRfQzFHRixGNSwsRiciIiVGLkY5RighIidGMyIiI0Y2RjtGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE2Mjg0MDkzNlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywoJSRfQzRHIiIjISM3IiIiJSRfQzJHISIlLChGJyIiKSEjPUYqRitGLkYlTTdSMApJNlJUQUJMRV9TQVZFLzE0MDU2ODM0MFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywoLSUkc2luRzYjLCQlInRHIiIjIyIiKEYsLSUkY29zR0YpIiIiLUYoNiMsJEYrIiIkIyEiKEY1LCgtRig2IywkRisiIiUjISImRjwtRjBGOiEiIkYyIyIiJkY1RiU=TTdSMApJNlJUQUJMRV9TQVZFLzE2Mjg0MTUxMlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyIiIiEiIkYlTTdSMApJNlJUQUJMRV9TQVZFLzE1OTY3Mzk0MFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyUjeDFHJSN4MkdGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1OTY1OTA1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsLSUkc2luRzYjLCQlInRHIiIkISIlLSUkY29zRzYjLCRGKyIiIyIiIi1GLzYjLCRGKyIiJUYzLUYoRjAjIiIoRjItRihGNSMiIiZGNywsRichIidGLkY3RjQhIiNGOCIjOUY7IyEiJkYyRiU=TTdSMApJNlJUQUJMRV9TQVZFLzE1OTg5NTM0NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIyUjeDFHJSN4MkdGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzE1OTk3MjE3NlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIiMiIywsLSUkc2luRzYjLCQlInRHJCIiJCIiISQhIiVGLi0lJGNvc0c2IywkRiskIiIjRi4iIiItRjI2IywkRiskIiIlRi5GNy1GKEYzJCIkXSQhIiMtRihGOSQiJEQiRkAsLEYnJCEiJ0YuRjFGO0Y4JEZARi5GPSQiIzlGLkZBJCEkXSNGQEYl