This lesson covers the concept of non-linear vibration analysis. It delves into the methods of solving non-linear differential equations, particularly using the Runge Kutta method. The lesson also discusses the use of MATLAB for solving these equations and plotting the responses. It further explains the concept of state space and phase portraits. The lesson also introduces the Lindstedt Poincare method and the method of multiple scales for solving non-linear equations of motion. It provides an in-depth explanation of these methods using examples and mathematical derivations. The lesson concludes with a discussion on the method of averaging for solving non-linear equations of motion.

- The Runge Kutta method is a numerical method used to solve non-linear differential equations.
- MATLAB can be used to solve these equations and plot the responses.
- State space and phase portraits are useful for studying the system's response.
- The Lindstedt Poincare method and the method of multiple scales are advanced methods for solving non-linear equations of motion.
- The method of averaging is another technique for solving non-linear equations of motion.

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