Rayleigh's quotient in vibrations analysis

The Rayleigh quotient represents a quick method to estimate the natural frequency of both discrete and continuous oscillating systems. ω n 2 ≈ V T ~ {\displaystyle \omega _{n}^{2}\approx {\frac {V}{\tilde {T}}}} where ω n {\displaystyle \omega _{n}} is the natural frequency of the nth mode, V {\displaystyle V} is the potential energy of the system and T ~ {\displaystyle {\tilde {T}}} is a property equivalent to the kinetic energy but with velocity replaced by position.

Source: Wikipedia — Rayleigh's quotient in vibrations analysis (CC BY-SA 4.0)