MAT2705-02/06 09F Quiz 10 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, MathCad).JSFH1. A coupled second order system of DEs with initial conditions is the following:
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 .a) Rewrite this system of DEs and its initial conditions in matrix form for the (column matrix!) vector variable 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 , identifying the coefficient matrix ALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= and forcing vector function LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbW92ZXJHRiQ2JS1GLDYlUSJGRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEtJlJpZ2h0QXJyb3c7RicvJSxwbGFjZWhvbGRlckdGOS9GO1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkcvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGRy8lKGxhcmdlb3BHRkcvJS5tb3ZhYmxlbGltaXRzR0ZHLyUnYWNjZW50R0ZHLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVi9GU0Y5RkNGK0ZD, namely: 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, 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 .
b) Use the Maple right click menu find the eigenvalues and eigenvectors of this coefficient matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Write them down identifying the eigenvalues LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIixGJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JUYuLUYjNiUtRjs2JFEiMkYnRjVGPkZARkJGNQ== and the corresponding matrix of eigenvectors 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.c) Evaluate the new components of the vectors 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 and 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 by left multiplication by the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4=.d) On the graph paper on the reverse side, draw in the two eigenvectors as arrows (label them) and their associated new coordinate lines 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, and the initial vectors 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 and 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 (label them!). Graphically determine their new components with respect to the new basis using your diagram, drawing in the parallelogram associated with their projections along the new basis vectors down to the new coordinate lines for each vector. Is your drawing consistent with your matrix calculated components? Explain.e) Introduce the 4 component vector variable 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, and re-express the DEs and initial conditions in the first order matrix form
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, 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 .solution 1. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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 vector form of this IVP is: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The coefficient matrix and its eigenvalues and eigenvectors are: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Fix the order of the eigenvectors:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUkobWZlbmNlZEdGJDYoLUYjNiMtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYnLUkkbXRkR0YkNigtSSNtbkdGJDYkUSI0RidGOS8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGXW8vJStncm91cGFsaWduR0Zdby8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0Zkby1GZW42KC1GIzYkLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZfcC1GaG42JFEiMkYnRjlGW29GXm9GYG9GYm9GZW9GW29GXm9GYG8tRlg2Jy1GZW42KC1GaG42JEZkb0Y5RltvRl5vRmBvRmJvRmVvRmZwRltvRl5vRmBvLyUmYWxpZ25HUSVheGlzRicvRlxvUSliYXNlbGluZUYnL0Zfb1EmcmlnaHRGJy9GYW9RJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGZ3EvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGYnIvJSZmcmFtZUdGYnIvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y9LyUtZXF1YWxjb2x1bW5zR0Y9LyUtZGlzcGxheXN0eWxlR0Y9LyUlc2lkZUdGYHEvJTBtaW5sYWJlbHNwYWNpbmdHRl9yRjkvSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zkcw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY2LUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY7Ni1RIjtGJ0Y+RkAvRkRGNEZFRkdGSUZLRk0vRlBRJjAuMGVtRicvRlNRLDAuMjc3Nzc3OGVtRictRjs2LVEifkYnRj5GQEZDRkVGR0ZJRktGTUZpbi9GU0ZqbkYrRl1vLUYvNiVRIkFGJ0YyRjVGXW9GLkZlbkZdb0YrRl1vLUkobWFjdGlvbkdGJDYkLUkobWZlbmNlZEdGJDYoLUYjNictRi82I1EhRictSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYmLUkkbXRkR0YkNigtRiM2Ji1GVTYkRlpGPi8lK2V4ZWN1dGFibGVHRkIvJSxwbGFjZWhvbGRlckdGNEY+LyUpcm93YWxpZ25HRl5wLyUsY29sdW1uYWxpZ25HRl5wLyUrZ3JvdXBhbGlnbkdGXnAvJShyb3dzcGFuR0ZXLyUrY29sdW1uc3BhbkdGV0ZgcUZicUZkcS1GY3A2Ji1GZnA2KC1GIzYmLUZVNiRRIjNGJ0Y+RlxxRl5xRj5GYHFGYnFGZHFGZnFGaHFGYHFGYnFGZHEvJSZhbGlnbkdRJWF4aXNGJy9GYXFRKWJhc2VsaW5lRicvRmNxUSdjZW50ZXJGJy9GZXFRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0Y0LyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGYHMvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGW3QvJSZmcmFtZUdGW3QvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0ZCLyUtZXF1YWxjb2x1bW5zR0ZCLyUtZGlzcGxheXN0eWxlR0ZCLyUlc2lkZUdRJnJpZ2h0RicvJTBtaW5sYWJlbHNwYWNpbmdHRmhzRlxwRlxxRj5GPi9JK21zZW1hbnRpY3NHRiRRKkNvbFZlY3RvckYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRl51LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJy1GOzYtUSIsRidGPkZARmhuRkVGR0ZJRktGTUZpbi9GU1EsMC4zMzMzMzMzZW1GJ0YrRl1vLUZlbzYkLUZobzYoLUYjNidGXHAtRmBwNjYtRmNwNiYtRmZwNigtRiM2J0Y6LUZVNiRRIjZGJ0Y+RlxxRl5xRj5GYHFGYnFGZHFGZnFGaHFGYHFGYnFGZHFGYnBGY3JGZnJGaHJGanJGXHNGXnNGYXNGY3NGZnNGaXNGXHRGXnRGYHRGY3RGZXRGZ3RGaXRGXHVGXHBGXHFGPkY+Rl51RmF1RmR1Rl51Rmd1RlxwRlxxRj4=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZicC1JI21pR0YkNiVRJXBsb3RGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2OS1GNjYmLUYjNictSSNtb0dGJDYtUSJ+RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlUtSSZtZnJhY0dGJDYoLUYsNiVRI3h4RidGL0YyLUYjNiMtSSNtbkdGJDYkUSI0RidGQi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY28vJSliZXZlbGxlZEdGRi1GPzYtUSIsRidGQkZEL0ZIRjFGSUZLRk1GT0ZRRlMvRldRLDAuMzMzMzMzM2VtRictRj82LVEqJnVtaW51czA7RidGQkZERkdGSUZLRk1GT0ZRL0ZUUSwwLjIyMjIyMjJlbUYnL0ZXRmJwLUZZNihGZW4tRiM2Iy1GW282JFEiMkYnRkJGXm9GYW9GZG9GZm9GQi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GPzYuRmpvRi9GMkZERltwRklGS0ZNRk9GUUZTRlxwRmVuLUY/Ni5RIj1GJ0YvRjJGREZHRklGS0ZNRk9GUS9GVFEsMC4yNzc3Nzc4ZW1GJy9GV0ZncS1GPzYuRmBwRi9GMkZERkdGSUZLRk1GT0ZRRmFwRmNwLUZbbzYlUSI1RidGL0YyLUY/Ni5RIy4uRidGL0YyRkRGR0ZJRktGTUZPRlFGYXBGVkZbckZhcS1GLDYlUSZjb2xvckYnRi9GMkZjcS1GLDYlUSZncmVlbkYnRi9GMkZhcS1GLDYlUSp0aGlja25lc3NGJ0YvRjJGY3EtRltvNiVGYG9GL0YyRmFxLUYsNiVRJXZpZXdGJ0YvRjJGY3FGaXFGW3JGXnJGW3JGQi1GPzYtUSI6RidGQkZERkdGSUZLRk1GT0ZRRmZxRmhxRj4tRiw2JVEncGxpbmVzRidGL0YyLUY/Ni1RKiZjb2xvbmVxO0YnRkJGREZHRklGS0ZNRk9GUUZmcUZocS1GLDYlUSIlRidGL0YyRl9zLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHRlUvJSZkZXB0aEdGYHQvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGPkY+LUYsNiVRI2ExRidGL0YyRmVzLUYsNiVRJmFycm93RidGL0YyLUY2NiQtRiM2Ky1GNjYmLUYjNiZGXnBGaHBGaG8tRltvNiRGYG9GQkZCL0ZccVEnJmxhbmc7RicvRl9xUScmcmFuZztGJ0Zoby1GLDYlUSZzaGFwZUYnRi9GMi1GPzYtRmVxRkJGREZHRklGS0ZNRk9GUUZmcUZocUZbdUZob0ZnckZfdkZocEZCRl9zRlt0Rj4tRiw2JVEjYTJGJ0YvRjJGZXNGW3UtRjY2JC1GIzYrLUY2NiYtRiM2JUZqbkZob0ZmdUZCRmh1Rmp1RmhvRlx2Rl92Rlt1RmhvRmdyRl92RmhwRkJGX3NGW3RGPkY+LUYsNiVRI2EzRidGL0YyRmVzRlt1LUY2NiQtRiM2MUZocEY+RmJ1RmhvRlx2Rl92Rlt1RmhvRmdyRl92RmZ1RmhvRmFyRl92LUYsNiVRJHJlZEYnRi9GMkZCRl9zRlt0Rj4tRiw2JVEjYTRGJ0YvRjJGZXNGW3UtRjY2JC1GIzYwLUYsNiNRIUYnRmh2RmhvRlx2Rl92Rlt1RmhvRmdyRl92RmZ1RmhvRmFyRl92RmN3RkJGX3NGW3RGPi1GLDYlUSNhNUYnRi9GMkZlc0ZbdS1GNjYkLUYjNi8tRjY2Ji1GIzYlLUZbbzYkUSIwRidGQkZoby1GW282JFEiM0YnRkJGQkZodUZqdUZob0ZcdkZfdkZbdUZob0ZnckZfdkZocEZob0ZhckZfdi1GLDYlUSVibHVlRidGL0YyRkJGX3NGW3RGPi1GLDYlUSNhNkYnRi9GMkZlc0ZbdS1GNjYkLUYjNi8tRjY2Ji1GIzYmRl5wLUZbbzYkUSI2RidGQkZob0ZbeUZCRmh1Rmp1RmhvRlx2Rl92Rlt1RmhvRmdyRl92RmhwRmhvRmFyRl92RmF5RkJGX3NGPkZbdEY+LUYsNiVRI2E3RidGL0YyRmVzRlt1LUY2NiQtRiM2Ly1GNjYmLUYjNiUtRltvNiRGXXJGQkZoby1GWTYoRmZ1RmZwRl5vRmFvRmRvRmZvRkJGaHVGanVGaG9GXHZGX3ZGW3VGaG9GZ3JGX3ZGaHBGaG9GYXJGX3ZGY3dGQkZfc0Y+Rlt0LUZcdDYmRl50RmF0RmN0L0ZmdFElYXV0b0YnRistRjY2JC1GIzYnLUY2NiYtRiM2KC1GNjYmRmp2RkJGW3FGXnFGaG8tRjY2JkZpeEZCRltxRl5xRmhvLUY2NiYtRiM2JkZecEZqbkZob0ZocEZCRltxRl5xRl14RkJGW3FGXnFGaG9GYXJGX3YtRiw2JVElZ3JheUYnRi9GMkZCRl9zRj4tRiw2JVEjcDRGJ0YvRjJGZXNGaHNGX3NGW3RGKy1GNjYkLUYjNictRjY2Ji1GIzYnLUY2NiYtRiM2J0ZecEZqbkZob0ZecEZmdUZCRltxRl5xRmhvLUY2NiZGXXpGQkZbcUZecUZoby1GNjYmRmR1RkJGW3FGXnFGQkZbcUZecUZob0ZhckZfdkZlXGxGQkZfc0Y+LUYsNiVRI3A1RidGL0YyRmVzRmhzRl9zRj5GW3RGW3RGYVtsLUYsNiZRKGRpc3BsYXlGJ0YvLyUrZXhlY3V0YWJsZUdGRkYyLUY2NiUtRiM2NkZic0Zob0Y+RmhcbEZob0ZbXmxGaG9GXHdGaG9GZndGaG9GaHRGaG9GYXZGaG9GYHhGaG9GZHlGaG9GYnpGYV5sRkI=The first blue vector along the vertical axis is clearly the first eigenvector plus twice the second eigenvector: components LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMkYnRjRGNEY0LyUlb3BlbkdRJyZsYW5nO0YnLyUmY2xvc2VHUScmcmFuZztGJ0Y0. The second blue vector along the horizontal axis is just minus the first eigenvector plus the second eigenvector, so components 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 .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2. 2nd order system, coupled harmonic oscillators (later)Now the second order system.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The two periods are related by a factor of 2; the longer period is therefore the common period, during which two oscillationss of the short period take place.The in phase (same sign components, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y+ has 4 times the amplitude of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+) eigenvector has the higher frequency and shorter period. The out of phase (opposite sign components, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y+ has 2 times the amplitude of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+) eigenvector has the higher frequency and shorter period. We plot them against each other (not requested) and versus the time for 1 common period.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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRLkxpbmVhckFsZ2VicmFGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiOkYnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVA==The new coordinates (first line) and the mode decomposition of the solution (second line), and their recombination to get the actual solution (third line):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gridline default plot 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