Vibration Problem

Solution of a system of second-order homogeneous ordinary differential equations with constant Coefficients of the form

where B is a Positive Definite Matrix. To solve the vibration problem,
1. Solve the Characteristic Equation of B to get Eigenvalues , ..., . Define .

2. Compute the corresponding Eigenvectors , ..., .

3. The normal modes of oscillation are given by , ..., , where , ..., and , ..., are arbitrary constants.

4. The general solution is .