This lesson covers the concept of the state-based method used in solving vibration problems. It delves into the technique of solving a vibration problem where continuous and lump parameter systems are involved. The lesson further explains the formulation known as the state-based solution method, which can be used for general types of damping. It also discusses the development of state-based equations, eigenvalues, and eigenvectors of the system. The lesson provides examples of single degree freedom and multi-degree freedom systems. It also proves whether the authority conditions of the eigenvectors in the state-based method exist or not.

- The state-based method is a technique used in solving vibration problems involving continuous and lump parameter systems.
- This method transforms the second-order system of dynamic equations into a first-order system, making the integration process simpler.
- The state-based method is particularly useful in problems where the control of vibration is required, such as in active control of vibration.
- The method can handle general types of damping, including non-proportional damping.
- The method has the existence of authority conditions of the eigenvectors.

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