Understanding System Response to Arbitrary Excitation — Lesson 3

This lesson covers the response of a system subjected to arbitrary excitation. It delves into the time response of a linear system, focusing on simple oscillator systems and systems with several degrees of freedom. The lesson explains the concept of Duhamel's integral and its application in time domain analysis for arbitrary excitation. It also discusses the response of a system to step input and the analysis of coupled systems. The lesson further explores the concept of eigenvalues and eigenvectors, and how they are used in the decoupling of system equations. An example of a two-degree freedom system is used to illustrate these concepts.

Video Highlights

02:42 - Impulse response function and its derivation for undamped and damped systems.
03:01 - Discussion on the time domain analysis of a coupled system with numerical examples.
06:39 - Concept of the Delta function or direct Delta function.
10:02 - Response of a single degree Freedom system subjected to unit impulse.
21:19 - Response of a damped oscillator to step input using Duhamel's integral.
39:11 - Concept of eigenvalues and eigenvectors in the context of natural frequencies and mode shapes.
52:16 - Response of a two-degree Freedom system without damping to initial conditions.

Key Takeaways

- The response of a system to arbitrary excitation can be analyzed using Duhamel's integral.
- The time response of a linear system can be focused on simple oscillator systems and systems with several degrees of freedom.
- Eigenvalues and eigenvectors play a crucial role in the decoupling of system equations.
- The response of a system to step input can be analyzed and examples can be used to illustrate these concepts.
- Understanding the concept of eigenvalues and eigenvectors is essential in the analysis of systems with several degrees of freedom.