MAT2705-02/06 10F 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).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=1. 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 explicit matrix form for the (column matrix!) vector variable 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 , identifying the coefficient matrix AJSFH 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 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 (ordered so that 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 so we all agree on the ordering of the new coordinates) and the corresponding matrix of eigenvectors 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. c) Evaluate the new components 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 and 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 of the vectors LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2JUYrLUkmbW92ZXJHRiQ2JS1GLDYnUSJ4RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y5LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJy1JI21vR0YkNi5RLSZSaWdodEFycm93O0YnLyUscGxhY2Vob2xkZXJHRjkvRj1RJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0ZMLyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmVuL0ZYRjlGSC1JKG1mZW5jZWRHRiQ2JC1GIzYkLUkjbW5HRiQ2JFEiMEYnRkhGSEZIRkg= and 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.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. JSFHJSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=JSFHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiNRIUYnLUklbXN1YkdGJDYlLUYsNiVRKFN0dWRlbnRGJ0YvRjJGOi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRjotRjY2Ji1GIzYlLUYsNiZRLkxpbmVhckFsZ2VicmFGJ0YvLyUrZXhlY3V0YWJsZUdRJmZhbHNlRidGMkZNL0YzUSdub3JtYWxGJ0ZQLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRjpGTUZQRlAtSSNtb0dGJDYtUSI6RidGUC8lJmZlbmNlR0ZPLyUqc2VwYXJhdG9yR0ZPLyUpc3RyZXRjaHlHRk8vJSpzeW1tZXRyaWNHRk8vJShsYXJnZW9wR0ZPLyUubW92YWJsZWxpbWl0c0dGTy8lJ2FjY2VudEdGTy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmZvRk1GUA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRkM2LVEifkYnRkBGRkZIRkpGTEZORlBGUi9GVVEmMC4wZW1GJy9GWEZnbkYrLUY2NiQtRiM2JS1GLDYlUShERXRvb2xzRidGL0YyRj1GQEZARkJGPUZALUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2Jy1GLDYlUSxUeXBlc2V0dGluZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzotRicvRjhRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlEtRiw2JVEpU2V0dGluZ3NGJ0Y0RjcvJStleGVjdXRhYmxlR0ZCRj5GKy1JKG1mZW5jZWRHRiQ2JC1GIzYnLUYsNiVRJnByaW1lRidGNEY3LUY7Ni1RIj1GJ0Y+RkBGQ0ZFRkdGSUZLRk1GT0ZSLUYsNiVRInRGJ0Y0RjdGV0Y+Rj4tRjs2LVEiOkYnRj5GQEZDRkVGR0ZJRktGTUZPRlJGV0Y+The vector form of this IVP is:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2I1EhRictSShtYWN0aW9uR0YkNiQtSShtZmVuY2VkR0YkNigtRiM2J0YrLUknbXRhYmxlR0YkNjYtSSRtdHJHRiQ2Ji1JJG10ZEdGJDYoLUYjNigtSSVtc3ViR0YkNiUtRiw2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0ZMUSdub3JtYWxGJ0ZIRksvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIidGJ0ZULyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Zpbi8lKXN0cmV0Y2h5R0Zpbi8lKnN5bW1ldHJpY0dGaW4vJShsYXJnZW9wR0Zpbi8lLm1vdmFibGVsaW1pdHNHRmluLyUnYWNjZW50R0Zpbi8lJ2xzcGFjZUdRLDAuMTExMTExMWVtRicvJSdyc3BhY2VHUSYwLjBlbUYnRlkvJStleGVjdXRhYmxlR0Zpbi8lLHBsYWNlaG9sZGVyR0ZKRlQvJSlyb3dhbGlnbkdGLi8lLGNvbHVtbmFsaWduR0YuLyUrZ3JvdXBhbGlnbkdGLi8lKHJvd3NwYW5HRlMvJStjb2x1bW5zcGFuR0ZTRmBwRmJwRmRwLUY7NiYtRj42KC1GIzYoLUZDNiVGRS1GIzYlLUZRNiRRIjJGJ0ZURkhGS0ZWRllGWUZccEZecEZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwLyUmYWxpZ25HUSVheGlzRicvRmFwUSliYXNlbGluZUYnL0ZjcFEnY2VudGVyRicvRmVwUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdGSi8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRmRyLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRl9zLyUmZnJhbWVHRl9zLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGaW4vJS1lcXVhbGNvbHVtbnNHRmluLyUtZGlzcGxheXN0eWxlR0Zpbi8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR0Zcc0YrRlxwRlRGVC9JK21zZW1hbnRpY3NHRiRRKkNvbFZlY3RvckYnLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmJ0LyUrYWN0aW9udHlwZUdRLnJ0YWJsZWFkZHJlc3NGJy1GWjYtUSI9RidGVEZnbkZqbkZcb0Zeb0Zgb0Zib0Zkby9GZ29RLDAuMjc3Nzc3OGVtRicvRmpvRmJ1LUYwNiQtRjM2KC1GIzYmRistRjg2Ni1GOzYnLUY+NigtRiM2JS1GWjYtUSomdW1pbnVzMDtGJ0ZURmduRmpuRlxvRl5vRmBvRmJvRmRvL0Znb1EsMC4yMjIyMjIyZW1GJy9Gam9GZnYtRlE2JFEiNUYnRlRGVEZgcEZicEZkcEZmcEZocC1GPjYoRmJxRmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwLUY7NictRj42KEZQRmBwRmJwRmRwRmZwRmhwLUY+NigtRiM2JUZidi1GUTYkUSI0RidGVEZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwRmdxRmpxL0ZjcEZfdEZeckZgckZickZlckZnckZqckZdc0Zgc0Zic0Zkc0Znc0Zpc0ZbdEZddEZgdEYrRlRGVC9GY3RRJ01hdHJpeEYnRmV0Rmh0Rml3Rlt1LUZaNi1RIn5GJ0ZURmduRmpuRlxvRl5vRmBvRmJvRmRvL0Znb0ZbcEZpby1GMDYkLUYzNigtRiM2JkYrLUY4NjYtRjs2Ji1GPjYoLUYjNiUtRkM2JUZFLUYjNiRGUEZURlZGK0ZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwLUY7NiYtRj42KC1GIzYlLUZDNiVGRS1GIzYkRmRxRlRGVkYrRlRGYHBGYnBGZHBGZnBGaHBGYHBGYnBGZHBGZ3FGanFGXHJGXnJGYHJGYnJGZXJGZ3JGanJGXXNGYHNGYnNGZHNGZ3NGaXNGW3RGXXRGYHRGK0ZURlRGYnRGZXRGaHRGYnRGW3UtRlo2LVEiK0YnRlRGZ25Gam5GXG9GXm9GYG9GYm9GZG9GZXZGZ3YtRjA2JC1GMzYoLUYjNidGKy1GODY2LUY7NiYtRj42KC1GIzYsRmJ2LUYsNiVRJGNvc0YnL0ZJRmluRlQtRlo2LVEiKEYnRlQvRmhuRkpGam4vRl1vRkpGXm9GYG9GYm9GZG8vRmdvUSwwLjE2NjY2NjdlbUYnL0Zqb0ZmW2xGZHFGW3gtRiw2JVEidEYnRkhGSy1GWjYtUSIpRidGVEZjW2xGam5GZFtsRl5vRmBvRmJvRmRvRmVbbEZnW2xGXHBGXnBGVEZgcEZicEZkcEZmcEZocEZgcEZicEZkcC1GOzYmLUY+NigtRiM2LUZkcUZbeEZcW2xGYFtsRmRxRlt4RmhbbEZbXGxGXHBGXnBGVEZgcEZicEZkcEZmcEZocEZgcEZicEZkcEZncUZqcUZcckZeckZgckZickZlckZnckZqckZdc0Zgc0Zic0Zkc0Znc0Zpc0ZbdEZddEZgdEYrRlxwRlRGVEZidEZldEZodEZidEZbdS1GWjYtUSIsRidGVEZnbi9GW29GSkZcb0Zeb0Zgb0Zib0Zkb0ZeeC9Gam9RLDAuMzMzMzMzM2VtRidGW3gtRjA2JC1GMzYoLUYjNiZGKy1GODY2LUY7NiYtRj42KC1GIzYnRl15RmBbbC1GUTYkRlhGVEZbXGxGVEZgcEZicEZkcEZmcEZocEZgcEZicEZkcC1GOzYmLUY+NigtRiM2J0ZneUZgW2xGaF1sRltcbEZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwRmdxRmpxRlxyRl5yRmByRmJyRmVyRmdyRmpyRl1zRmBzRmJzRmRzRmdzRmlzRlt0Rl10RmB0RitGVEZURmJ0RmV0Rmh0RmJ0Rlt1Rl51LUYwNiQtRjM2KC1GIzYnRistRjg2Ni1GOzYmLUY+NigtRiM2J0ZidkZkcUZccEZecEZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwLUY7NiYtRj42KC1GIzYmRmV3RlxwRl5wRlRGYHBGYnBGZHBGZnBGaHBGYHBGYnBGZHBGZ3FGanFGXHJGXnJGYHJGYnJGZXJGZ3JGanJGXXNGYHNGYnNGZHNGZ3NGaXNGW3RGXXRGYHRGK0ZccEZURlRGYnRGZXRGaHRGYnRGW3VGZFxsRlt4LUYjNihGKy1GMDYkLUYzNigtRiM2JkYrLUY4NjYtRjs2Ji1GPjYoLUYjNihGXXlGWUZgW2xGaF1sRltcbEZURmBwRmJwRmRwRmZwRmhwRmBwRmJwRmRwLUY7NiYtRj42KC1GIzYoRmd5RllGYFtsRmhdbEZbXGxGVEZgcEZicEZkcEZmcEZocEZgcEZicEZkcEZncUZqcUZcckZeckZgckZickZlckZnckZqckZdc0Zgc0Zic0Zkc0Znc0Zpc0ZbdEZddEZgdEYrRlRGVEZidEZldEZodEZidEZbdUZedS1GMDYkLUYzNigtRiM2JkYrLUY4NjYtRjs2Ji1GPjYoLUYjNiRGZXdGVEZgcEZicEZkcEZmcEZocEZgcEZicEZkcC1GOzYmLUY+NihGX3lGYHBGYnBGZHBGZnBGaHBGYHBGYnBGZHBGZ3FGanFGXHJGXnJGYHJGYnJGZXJGZ3JGanJGXXNGYHNGYnNGZHNGZ3NGaXNGW3RGXXRGYHRGK0ZURlRGYnRGZXRGaHRGYnRGW3VGK0ZURitGXHBGVA==coming up with the matrix 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JSFHThe coefficient matrix and its eigenvalues and eigenvectors are: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 the order of the eigenvectors: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d)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 first blue vector (left) is clearly twice the first eigenvector plus twice the second eigenvector: components LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYmLUYjNiYtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY0RjQvJSVvcGVuR1EnJmxhbmc7RicvJSZjbG9zZUdRJyZyYW5nO0YnRjQ=. The second(right) is just twice the first eigenvector minus the second eigenvector, so components 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 . The driving vector is along the first blue vector.
e) The reduced system is: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JSFH2. 2nd order system, coupled harmonic oscillators (later)Now the second order system.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 two periods are related by a factor of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRictSSZtc3FydEdGJDYjLUYjNiQtSSNtbkdGJDYkUSIyRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRjhGOA==; there is no common period.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): TO EDIT: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 default plot 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