Abstract: The differential equation of motion of the system with many identical pendulums is derived by using Lagrange＇ equation.Based on properties of three diagonal matrixes,the recursion expressions of characteristic polynomial and mode vectors of the vibration system are given.Moreover,taking three identical pendulums as examples,we show the application of the result and confirm the result in the reference [3] with this method.

Key words: many identical pendulums, free vibration, three diagonal matrixes, characteristic polynomial, mode vectors