Things that vibrate have natural modes of vibration. A particular vibrational pattern can be decomposed into a time-varying linear combination of these modes. T

Things that vibrate have natural modes of vibration. A particular vibrational pattern can be decomposed into a time-varying linear combination of these modes. The modes of vibration are eigenfunctions and the frequencies at which they vibrate are the square root of the corresponding eigenvalues. You can look up a vibrating drum head (circular membrane) for a simple example.