This lesson covers the fundamentals of non-linear vibration, focusing on the linear and non-linear equations of motion. It delves into the superposition rule, which distinguishes between linear and non-linear equations. The lesson also explores the application of the superposition rule in linear and non-linear systems. It provides references to various books on non-linear vibration, such as 'Non-Linear Oscillations' by Nape and DT Muk, and 'Applied Non-Linear Dynamics' by H Nape and B Balachandran. These resources can further enhance understanding of the topic.

- The superposition rule, which separates linear and non-linear equations, involves the application of homogeneity and additive properties.
- The homogeneity property states that if a force alpha FT is applied to a system and the response is alpha XT, it satisfies the homogeneity rule.
- The additive property states that if forces F1 and F2 are applied to a system, the response must be the sum of the responses to each force individually.

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