Eigenvalue

Vibration analysis

Eigenvalue problems occur naturally in the vibration analysis of mechanical structures with many degrees of freedom. The eigenvalues are the natural frequencies (or eigenfrequencies) of vibration, and the eigenvectors are the shapes of these vibrational modes. In particular, undamped vibration is governed by $${\displaystyle m{\ddot {x}}+kx=0}$$ or $${\displaystyle m{\ddot {x}}=-kx}$$