LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnMAT2705-01/04 07S Quiz 8 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).
1. IVP: 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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2MFEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSVmb3JtR1EhRicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGRi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1GLDYwUSIuRidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSZpbmZpeEYnRkRGR0ZJRkw=
For the 2 mass 3 spring problem let 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set 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 in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUwZm9udF9zdHlsZV9uYW1lR1EoMkR+TWF0aEYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjJRIj1GJ0YvRjJGNS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPi8lKXN0cmV0Y2h5R0Y+LyUqc3ltbWV0cmljR0Y+LyUobGFyZ2VvcEdGPi8lLm1vdmFibGVsaW1pdHNHRj4vJSdhY2NlbnRHRj4vJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRlAvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictSShtZmVuY2VkR0YkNiotRiM2JS1GLDYmUSFGJ0YvRjJGNS1JJ210YWJsZUdGJDY2LUkkbXRyR0YkNictSSRtdGRHRiQ2KC1GIzYlLUY5NjJRKiZ1bWludXMwO0YnRi9GMkY1RjxGP0ZBRkNGRUZHRklGSy9GT1EwbWVkaXVtbWF0aHNwYWNlRicvRlJGam9GU0ZWLUY5NjJRIn5GJ0YvRjJGNUY8Rj9GQUZDRkVGR0ZJL0ZMRmpuL0ZPUSQwZW1GJy9GUkZhcEZTRlYtSSZtZnJhY0dGJDYoLUYjNiZGXHAtSSVtc3ViR0YkNiUtRiw2JlEia0YnRi9GMkY1LUYjNiMtSSNtbkdGJDYmRlVGL0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GOTYyUSIrRidGL0YyRjVGPEY/RkFGQ0ZFRkdGSUZLRmlvRltwRlNGVi1GaXA2JUZbcS1GIzYjLUZhcTYmUSIyRidGL0YyRjVGY3EtRiM2Iy1GaXA2JS1GLDYmUSJtRidGL0YyRjVGXnFGY3EvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxzLyUpYmV2ZWxsZWRHRj4vJSlyb3dhbGlnbkdGam4vJSxjb2x1bW5hbGlnbkdGam4vJStncm91cGFsaWduR0Zqbi8lKHJvd3NwYW5HRmlyLyUrY29sdW1uc3BhbkdGaXItRmJvNigtRmRwNigtRiM2I0ZpcUZgckZnckZqckZdc0Zfc0Zhc0Zjc0Zlc0Znc0Zpc0Zhc0Zjc0Zlcy1GX282Jy1GYm82KC1GZHA2KEZfdC1GIzYjLUZpcDYlRmRyRltyRmNxRmdyRmpyRl1zRl9zRmFzRmNzRmVzRmdzRmlzLUZibzYoLUYjNiVGZm9GXHAtRmRwNigtRiM2JkZccEZpcUZmcS1GaXA2JUZbcS1GIzYjLUZhcTYmUSIzRidGL0YyRjVGY3FGZ3RGZ3JGanJGXXNGX3NGYXNGY3NGZXNGZ3NGaXNGYXNGY3NGZXMvJSZhbGlnbkdRJWF4aXNGJy9GYnNRKWJhc2VsaW5lRicvRmRzRlxzL0Zmc1EnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHRjEvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zmdi8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zhdy8lJmZyYW1lR0Zhdy8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHRj4vJS1lcXVhbGNvbHVtbnNHRj4vJS1kaXNwbGF5c3R5bGVHRj4vJSVzaWRlR1EmcmlnaHRGJy8lMG1pbmxhYmVsc3BhY2luZ0dGXndGaG5GL0YyRjUvSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZkeC1GOTYxRl5wRi9GNUY8Rj9GQUZDRkVGR0ZJRl9wRmBwRmJwRlNGVi1GOTYwUSIuRicvRjZRJ25vcm1hbEYnRjxGP0ZBRkNGRUZHRklGS0ZgcEZicEZTRlY=The eigenvalues of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== are 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 and the corresponding matrix of eigenvectors is 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. a) Introducing the coordinate change 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 , derive or remember (correctly) the DE for 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. b) Write out and solve the decoupled equations for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn and then evaluate 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 .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2MFEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSVmb3JtR1EhRicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGRi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJw==c) Impose the initial conditions on your general solution and express your final answer first in the eigenvector form 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 which shows the two modes of the system and then in the scalar form 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...,LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2MFEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSVmb3JtR1EhRicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGRi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JJW1zdWJHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRictRiM2Iy1JI21uR0YkNiRRIjJGJ0YvLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRiw2MFEiPUYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEmaW5maXhGJy9GRVEvdGhpY2ttYXRoc3BhY2VGJy9GSEZkb0ZJRkw=...LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW9HRiQ2MFEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSVmb3JtR1EhRicvJSdsc3BhY2VHUSQwZW1GJy8lJ3JzcGFjZUdGRi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJw==where all like terms have been combined.