Method of Multiple Scales — Lesson 2

This lesson covers the application of the method of multiple scales to solve non-linear differential equations. The instructor discusses the solution of non-linear differential equations using perturbation methods, particularly the straightforward expansion, the Lindstedt Poincare method, and the method of multiple scales. The lesson also explains the concept of different time scales and how they are used in the governing equation of motion. The instructor further elaborates on the concept of non-linear vibration, using the example of a spring mass damper system subjected to quadratic and cubic non-linearity. The lesson concludes with an assignment for students to plot the response of free vibration of a system with quadratic and cubic nonlinearity.

Video Highlights

00:59 - Time scales and their application in the governing equation of motion
03:01 - Method of multiple scales applied to force vibration
38:16 - Parametrically excited system and its application 
47:16 - Trivial and non-trivial steady-state responses

Key Takeaways

- The method of multiple scales is a powerful tool for solving non-linear differential equations.
- Different time scales can be used in the governing equation of motion to account for different factors affecting the system.
- The concept of non-linear vibration can be understood using the example of a spring mass damper system subjected to quadratic and cubic non-linearity.
- The solution of the first equation in the form of X1 equal to AT1T2 provides a clear understanding of the method of multiple scales.
- The assignment given to students to plot the response of free vibration of a system with quadratic and cubic nonlinearity helps in practical understanding of the concepts.