coupled 2 mass spring system with dampingWe introduce a variable damping coefficient LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn (which leads to a multiple of the identity matrix for the 2x2 matrix acceleration equation, so that diagonalizing the Hookes law coefficient matrix decouples the DEs, as a toy example of using reduction of order. [Still to do]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JSFHeigenvectorsVector form: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eigenvectors: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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYmLUkjbWlHRiQ2JlEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyU2c2VsZWN0aW9uLXBsYWNlaG9sZGVyR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiVRImlGJy9GM0Y3L0Y5USdpdGFsaWNGJy8lLHBsYWNlaG9sZGVyR0Y3RjgvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy9JK21zZW1hbnRpY3NHRiRRJ2F0b21pY0YnRjg==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMkYnRi9GLw==Initial conditions at rest at equilibrium when needed.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY7LUkjbWlHRiQ2JVEmaW5pdHNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiQtSSNtbkdGJDYkUSIxRidGOUY5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GWDYkRmduRjlGOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRl1vLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRlA2JUZSLUYjNiQtRlg2JFEiMkYnRjlGOUZlbkZobkZfb0Zdb0Zib0ZPLUY2Ni1RIidGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTExMTExMWVtRicvRk5GZ29GaG5GX29GXW9GYm9Gam9GYXBGaG5GX29GXW8vJStleGVjdXRhYmxlR0Y9Rjk=We include a variable driving frequency, to explore the region containing the eigenfrequencies 1 and 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
SSJjRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t)]),t = 0 .. N*Pi,color = [red, blue],view = -L .. L), ':-Plot0', [':-c', ':-omega', ':-L', ':-N'], ':-sliders'=["Sliderc", "Slideromega", "SliderL4", "SliderN4"], ':-labels'=["Labelc", "Labelomega", "LabelL4", "LabelN4"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],L=handlertab[L],N=handlertab[N]]);
#
# End of autogenerated code.
#
SSZvbWVnYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t)]),t = 0 .. N*Pi,color = [red, blue],view = -L .. L), ':-Plot0', [':-c', ':-omega', ':-L', ':-N'], ':-sliders'=["Sliderc", "Slideromega", "SliderL4", "SliderN4"], ':-labels'=["Labelc", "Labelomega", "LabelL4", "LabelN4"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],L=handlertab[L],N=handlertab[N]]);
#
# End of autogenerated code.
#
SSJMRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t)]),t = 0 .. N*Pi,color = [red, blue],view = -L .. L), ':-Plot0', [':-c', ':-omega', ':-L', ':-N'], ':-sliders'=["Sliderc", "Slideromega", "SliderL4", "SliderN4"], ':-labels'=["Labelc", "Labelomega", "LabelL4", "LabelN4"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],L=handlertab[L],N=handlertab[N]]);
#
# End of autogenerated code.
#
SSJORzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t)]),t = 0 .. N*Pi,color = [red, blue],view = -L .. L), ':-Plot0', [':-c', ':-omega', ':-L', ':-N'], ':-sliders'=["Sliderc", "Slideromega", "SliderL4", "SliderN4"], ':-labels'=["Labelc", "Labelomega", "LabelL4", "LabelN4"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],L=handlertab[L],N=handlertab[N]]);
#
# End of autogenerated code.
#
Lengthen the time interval (number N of periods of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctSSNtaUdGJDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGOEYvLyUrZXhlY3V0YWJsZUdGOEYv) to see longer term behavior and expand the vertical window L when the amplitudes grow near the eigenfrequencies. This shows clearly the resonance with no damping, and how damping affects it making the system more and more sluggish.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
SSJjRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot1', [':-c', ':-omega', ':-N', ':-L'], ':-sliders'=["Sliderc1", "Slideromega1", "SliderN", "SliderL"], ':-labels'=["Labelc1", "Labelomega1", "LabelN", "LabelL"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],N=handlertab[N],L=handlertab[L]]);
#
# End of autogenerated code.
#
SSZvbWVnYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot1', [':-c', ':-omega', ':-N', ':-L'], ':-sliders'=["Sliderc1", "Slideromega1", "SliderN", "SliderL"], ':-labels'=["Labelc1", "Labelomega1", "LabelN", "LabelL"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],N=handlertab[N],L=handlertab[L]]);
#
# End of autogenerated code.
#
SSJORzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot1', [':-c', ':-omega', ':-N', ':-L'], ':-sliders'=["Sliderc1", "Slideromega1", "SliderN", "SliderL"], ':-labels'=["Labelc1", "Labelomega1", "LabelN", "LabelL"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],N=handlertab[N],L=handlertab[L]]);
#
# End of autogenerated code.
#
SSJMRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = cos(omega*t), x[1](0) = 0, x[2](0) = 0, D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot1', [':-c', ':-omega', ':-N', ':-L'], ':-sliders'=["Sliderc1", "Slideromega1", "SliderN", "SliderL"], ':-labels'=["Labelc1", "Labelomega1", "LabelN", "LabelL"],':-isplot'=true, ':-handlers'=[c=handlertab[c],omega=handlertab[omega],N=handlertab[N],L=handlertab[L]]);
#
# End of autogenerated code.
#
For the undriven system explore release from rest around unit circle parametrized by the angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg== .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
SSJjRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = 0, x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot2', [':-c', ':-N', ':-L', ':-alpha'], ':-sliders'=["Sliderc2", "SliderN1", "SliderL1", "Slideralpha"], ':-labels'=["Labelc2", "LabelN1", "LabelL1", "Labelalpha"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],alpha=handlertab[alpha]]);
#
# End of autogenerated code.
#
SSJORzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = 0, x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot2', [':-c', ':-N', ':-L', ':-alpha'], ':-sliders'=["Sliderc2", "SliderN1", "SliderL1", "Slideralpha"], ':-labels'=["Labelc2", "LabelN1", "LabelL1", "Labelalpha"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],alpha=handlertab[alpha]]);
#
# End of autogenerated code.
#
SSJMRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = 0, x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot2', [':-c', ':-N', ':-L', ':-alpha'], ':-sliders'=["Sliderc2", "SliderN1", "SliderL1", "Slideralpha"], ':-labels'=["Labelc2", "LabelN1", "LabelL1", "Labelalpha"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],alpha=handlertab[alpha]]);
#
# End of autogenerated code.
#
SSZhbHBoYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = 0, x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot2', [':-c', ':-N', ':-L', ':-alpha'], ':-sliders'=["Sliderc2", "SliderN1", "SliderL1", "Slideralpha"], ':-labels'=["Labelc2", "LabelN1", "LabelL1", "Labelalpha"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],alpha=handlertab[alpha]]);
#
# End of autogenerated code.
#
For the driven system explore release from rest around unit circle parametrized by the angle LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHRjFGMg== and turn on the driving function amplitude LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJw==.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY9LUkjbWlHRiQ2JVEmaW5pdHNGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JS1GLDYlUSJ4RidGL0YyLUYjNiQtSSNtbkdGJDYkUSIxRidGOUY5LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GWDYkRmduRjlGOUY5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUYsNiVRJGNvc0YnL0YwRj1GOS1GaW42JC1GIzYlLUYsNiVRJyYjOTQ1O0YnRmVvRjkvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZQNiVGUi1GIzYkLUZYNiRRIjJGJ0Y5RjlGZW5GaG5GX28tRiw2JVEkc2luRidGZW9GOUZmb0ZfcEZPLUY2Ni1RIidGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTExMTExMWVtRicvRk5GZHBGaG5GX29GXW9GX3BGZ3BGYXFGaG5GX29GXW9GXXBGOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVElZGVxc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYjNlMtRiw2I1EhRictSSVtc3ViR0YkNiUtRiw2JVEieEYnRi9GMi1GIzYkLUkjbW5HRiQ2JFEiMUYnRjlGOS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIidGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTExMTExMWVtRicvRk5RJjAuMGVtRidGXW8tSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGL0YyRjlGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmBwLUYsNiVRImNGJ0YvRjItRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS0Zjb0Zib0ZlcEZURl1vRmRvRlxwLUkmbWZyYWNHRiQ2KC1GZ242JFEiNUYnRjktRiM2JC1GZ242JFEiMkYnRjlGOS8lLmxpbmV0aGlja25lc3NHRmluLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmhxLyUpYmV2ZWxsZWRHRj1GZXBGVEZkby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRl9wRmFwLUZqcDYoLUZnbjYkUSIzRidGOUZfcUZkcUZmcUZpcUZbckZlcC1GVTYlRldGX3FGam5GZG8tRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRmduNiRGXG9GOS1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRmhwL0ZOUSwwLjMzMzMzMzNlbUYnRmVwRmVyRl1vRl1vRmRvRlxwRmJwRmVwRmVwRmVyRl1vRmRvRl1yRmVwRmByRmVwRlRGZG9GXHBGaXBGZXBGZXJGZG9GOUZnci1GLDYlUSJmRidGL0YyRmVwLUYsNiVRJGNvc0YnL0YwRj1GOS1GZW82JC1GIzYmLUYsNiVRKCZvbWVnYTtGJ0Zoc0Y5RmVwRmlvRjlGOS8lK2V4ZWN1dGFibGVHRj1GOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoRXhwbG9yZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzZYLUYsNiNRIUYnLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRkIvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRj42JkZARkNGRi9GSVElYXV0b0YnLUYsNiVRJXBsb3RGJ0YvRjItRjY2JC1GIzYwRjpGPUZLLUYsNiVRJXN1YnNGJ0YvRjItRjY2JC1GIzYnLUYsNiVRJ2Rzb2x2ZUYnRi9GMi1GNjYkLUYjNiYtRjY2Ji1GIzYmLUYsNiVRJWRlcXNGJ0YvRjItSSNtb0dGJDYtUSIsRicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRl1wLyUqc3ltbWV0cmljR0ZdcC8lKGxhcmdlb3BHRl1wLyUubW92YWJsZWxpbWl0c0dGXXAvJSdhY2NlbnRHRl1wLyUnbHNwYWNlR0ZFLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSZpbml0c0YnRi9GMkZpb0Zpby8lJW9wZW5HUSJ8ZnJGJy8lJmNsb3NlR1EifGhyRidGZW8tRjY2Ji1GIzYoLUklbXN1YkdGJDYlLUYsNiVRInhGJ0YvRjItRiM2JC1JI21uR0YkNiRRIjFGJ0Zpb0Zpby8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY2NiQtRiM2JC1GLDYlUSJ0RidGL0YyRmlvRmlvRmVvLUZdcjYlRl9yLUYjNiQtRmVyNiRRIjJGJ0Zpb0Zpb0ZockZbc0Zpb0Zpb0ZicUZlcUZpb0Zpb0Zlby1GNjYmLUYjNjFGXHJGW3NGZW9GYnNGW3NGZW8tRmZvNi1RIn5GJ0Zpb0ZbcC9GX3BGXXBGYHBGYnBGZHBGZnBGaHBGanAvRl1xRkVGX3MtRmZvNi1RIj1GJ0Zpb0ZbcEZgdEZgcEZicEZkcEZmcEZocC9GW3FRLDAuMjc3Nzc3OGVtRicvRl1xRmZ0LUZlcjYkRmpyRmlvLUZmbzYtUSMuLkYnRmlvRltwRmB0RmBwRmJwRmRwRmZwRmhwL0ZbcVEsMC4yMjIyMjIyZW1GJ0ZhdC1GLDYlUSJORidGL0YyRl10LUYsNiVRJSZwaTtGJy9GMEZdcEZpb0Zpb0Zpby9GY3FRIltGJy9GZnFRIl1GJ0Zpb0Zpb0Zlby1GLDYlUSZjb2xvckYnRi9GMkZidC1GNjYmLUYjNiYtRiw2JVEkcmVkRidGL0YyRmVvLUYsNiVRJWJsdWVGJ0YvRjJGaW9GaW9GZnVGaHVGZW8tRiw2JVEldmlld0YnRi9GMkZidC1GNjYmLUYjNiwtRmZvNi1RKiZ1bWludXMwO0YnRmlvRltwRmB0RmBwRmJwRmRwRmZwRmhwRl11L0ZdcUZedS1GLDYlUSJMRidGL0YyRmp0RmJ3RmVvRl53RmJ3Rmp0RmJ3RmlvRmlvRmZ1Rmh1RmlvRmlvRmVvLUYsNiVRImNGJ0YvRjJGYnRGaHRGanQtRmVyNiRRJDEuMEYnRmlvRmVvRl91RmJ0LUZlcjYkUSI2RidGaW9GanQtRmVyNiRRIzIwRidGaW9GZW9GXXRGYndGYnRGaHdGanQtRmVyNiRRJDYuMEYnRmlvRmVvLUYsNiVRImZGJ0YvRjJGYnQtRmVyNiRRJDAuMEYnRmlvRmp0Rmh3RmVvRl10LUYsNiVRJyYjOTQ1O0YnRmV1RmlvRmJ0Rmh0Rmp0LUZlcjYkUSU2LjI4RidGaW9GZW9GXXQtRiw2JVEnJiM5Njk7RidGZXVGaW9GYnQtRmVyNiRRJDAuNUYnRmlvRmp0RmZzRmVvLUYsNiVRKnBsYWNlbWVudEYnRi9GMkZidC1GLDYlUSZyaWdodEYnRi9GMkZlb0ZddC1GLDYlUS5pbml0aWFsdmFsdWVzRidGL0YyRmJ0LUY2NiYtRiM2LkZld0ZidEZodEZlb0ZfdUZidEZbeEZlb0Zid0ZidEZmc0Zpb0Zpb0ZmdUZodUZpb0Zpb0Y6LyUrZXhlY3V0YWJsZUdGXXBGaW8=
SSJjRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJORzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJMRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJmRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSZhbHBoYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSZvbWVnYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t), x[1](0) = cos(alpha), x[2](0) = sin(alpha), D(x[1])(0) = 0, D(x[2])(0) = 0},{x[1](t), x[2](t)}),[x[1](t), x[2](t), t = 0 .. N*Pi]),color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot4', [':-c', ':-N', ':-L', ':-f', ':-alpha', ':-omega'], ':-sliders'=["Sliderc4", "SliderN2", "SliderL2", "Sliderf", "Slideralpha1", "Slideromega2"], ':-labels'=["Labelc4", "LabelN2", "LabelL2", "Labelf", "Labelalpha1", "Labelomega2"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],alpha=handlertab[alpha],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
For the driven system explore the response solution from the driving force only (removing the homogeneous solution by setting the arbitrary constants to zero):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
SSJjRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(subs(_C1 = 0,_C2 = 0,_C3 = 0,_C4 = 0,dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t)},{x[1](t), x[2](t)})),[x[1](t), x[2](t), t = 0 .. N*Pi]),gridlines = true,color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot5', [':-c', ':-N', ':-L', ':-f', ':-omega'], ':-sliders'=["Sliderc5", "SliderN3", "SliderL3", "Sliderf1", "Slideromega3"], ':-labels'=["Labelc5", "LabelN3", "LabelL3", "Labelf1", "Labelomega3"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJORzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(subs(_C1 = 0,_C2 = 0,_C3 = 0,_C4 = 0,dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t)},{x[1](t), x[2](t)})),[x[1](t), x[2](t), t = 0 .. N*Pi]),gridlines = true,color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot5', [':-c', ':-N', ':-L', ':-f', ':-omega'], ':-sliders'=["Sliderc5", "SliderN3", "SliderL3", "Sliderf1", "Slideromega3"], ':-labels'=["Labelc5", "LabelN3", "LabelL3", "Labelf1", "Labelomega3"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJMRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(subs(_C1 = 0,_C2 = 0,_C3 = 0,_C4 = 0,dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t)},{x[1](t), x[2](t)})),[x[1](t), x[2](t), t = 0 .. N*Pi]),gridlines = true,color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot5', [':-c', ':-N', ':-L', ':-f', ':-omega'], ':-sliders'=["Sliderc5", "SliderN3", "SliderL3", "Sliderf1", "Slideromega3"], ':-labels'=["Labelc5", "LabelN3", "LabelL3", "Labelf1", "Labelomega3"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSJmRzYi#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(subs(_C1 = 0,_C2 = 0,_C3 = 0,_C4 = 0,dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t)},{x[1](t), x[2](t)})),[x[1](t), x[2](t), t = 0 .. N*Pi]),gridlines = true,color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot5', [':-c', ':-N', ':-L', ':-f', ':-omega'], ':-sliders'=["Sliderc5", "SliderN3", "SliderL3", "Sliderf1", "Slideromega3"], ':-labels'=["Labelc5", "LabelN3", "LabelL3", "Labelf1", "Labelomega3"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
SSZvbWVnYUc2Ig==#
# The following code is autogenerated by the Explore command. Do not edit.
#
Explore:-Runtime:-Update( plot(subs(subs(_C1 = 0,_C2 = 0,_C3 = 0,_C4 = 0,dsolve({(D@@2)(x[1])(t)+c*D(x[1])(t)+5/2*x[1](t)-3/2*x[2](t) = 0, (D@@2)(x[2])(t)+c*D(x[2])(t)-3/2*x[1](t)+5/2*x[2](t) = f*cos(omega*t)},{x[1](t), x[2](t)})),[x[1](t), x[2](t), t = 0 .. N*Pi]),gridlines = true,color = [red, blue],view = [-L .. L, -L .. L]), ':-Plot5', [':-c', ':-N', ':-L', ':-f', ':-omega'], ':-sliders'=["Sliderc5", "SliderN3", "SliderL3", "Sliderf1", "Slideromega3"], ':-labels'=["Labelc5", "LabelN3", "LabelL3", "Labelf1", "Labelomega3"],':-isplot'=true, ':-handlers'=[c=handlertab[c],N=handlertab[N],L=handlertab[L],f=handlertab[f],omega=handlertab[omega]]);
#
# End of autogenerated code.
#
This shows that the response is big along the corresponding eigendirection when the frequency passes through each eigenfrequency. Turning on just a little damping lessens the response, and the narrow elliptical path squeezes to the eigenline line segment when the damping coefficient goes to zero. Increasing the forcing function amplitude only magnifies the path (linearity!).