The axes not analyzed
(Modeled on "The Road Not Taken," by Robert Frost)
Two masses oscillated on a spring of wood,
And sorry that I could not separate both
And be in Descartes' plane, long I stood
And looked down Hilbert space as far as I could
To where initial positions were plotted on axes' spokes;
Then looked again, new axes just as fair,
And having perhaps the better claim,
Because normal mode eigenvectors were plotted there;
And as for that the analysis where
Normal modes superpose shall be the game,
Though both axes equally lay
In space no intro-physics work had penciled black.
Oh, I kept the first axes for another day!
Yet knowing inner products of eigenvectors and position lead the way,
I doubted I should need to come back.
I will multiply these coefficients with eigenvectors P and B
And let them oscillate in time for ages and ages hence.
Two masses oscillated on a spring, and me -–
I superposed their normal modes with glee
And that has made all the difference.