Time Domain Analysis of Linear System - Harmonic input — Lesson 2

This lesson covers the concept of vibration in continuous systems, focusing on the time domain analysis of linear systems subjected to harmonic input. It explains the difference between discrete and continuous systems, the modeling of dynamic problems, and the impact of damping on system responses. The lesson also introduces the magnification factor and resonance phenomena, and discusses a special technique known as the Half Power Bandwidth for determining the damping ratio. It further explains the concept of logarithmic decrement and how it can be used to measure damping from experimental data. The lesson concludes with a discussion on the frequency response function and how it can be used to determine the damping factor.

Video Highlights

01:37 - Time domain analysis of linear systems.
05:11 - Explanation of the general approach for time domain analysis.
39:16 - Discussion on the concept of logarithmic decrement for measuring damping.
48:38 - Discussion on the behavior of a dynamic system subjected to harmonic force.
52:20 - Explanation of the concept of frequency response function.

Key Takeaways

- Vibration in continuous systems can be analyzed using time domain analysis.
- Damping plays a significant role in the response of a system, affecting the decay of time response and the nature of oscillations.
- The magnification factor and resonance phenomena are crucial concepts in understanding system responses.
- The Half Power Bandwidth technique is a useful tool for determining the damping ratio.
- The logarithmic decrement can be used to measure damping from experimental data.
- The frequency response function can be used to determine the damping factor.