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In applied mathematics, mode shapes are a manifestation of eigenvectors which describe the relative displacement of two or more elements in a mechanical system [1] or wave front [2].
See also

Normal mode
Harmonic oscillator

References

College, Erik Cheever, Swarthmore. "Vibration Animations". lpsa.swarthmore.edu.
Bobkov, K. K.; Bubnov, M. M.; Aleshkina, S. S.; Likhachev, M. E. (22 May 2018). "Long-term mode shape degradation in large mode area Yb-doped pulsed fiber amplifiers". Laser Physics Letters. 14 (1): 015102. doi:10.1088/1612-202X/14/1/015102 – via Institute of Physics.

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