Rayleigh's quotient in vibrations analysis

Rayleigh's quotient is a method used in the analysis of vibrations, particularly in determining the natural frequencies of a system. It is derived from the Rayleigh method, which utilizes energy principles to approximate the natural frequencies of a vibrating system. The Rayleigh quotient \( R \) for a dynamical system can be expressed as: \[ R = \frac{U}{K} \] Where: - \( U \) is the potential energy of the system in a given mode of vibration.