Structural Mechanics

The equations of motion for a two degrees of freedom undamped spring -mass system are: mẍ1 + 2kx1 - kx2 = 0 mẍ2 - kx1 + 2kx2 = 0 where m and k represent mass and stiffness respectively, in corresponding SI units, and x1 and x2 are the degrees of freedom. The larger of the two natural frequencies is given by: 𝜔 = 𝛼√ k m rad/s. The value of 𝛼 is ________ (rounded off to 2 decimal places).