Impulse Response Function — Lesson 1

This lesson covers the concept of impulse response function in the context of a mass spring dashpot system. It begins with a discussion on the response of a system to an impulse and how to calculate the response to arbitrary loading. The lesson then delves into the derivation of the impulse response function, explaining how it can be used to determine the response of a system to an arbitrary forcing function. The lesson also introduces the concept of a convolution integral, which is used to calculate the total response of a system to an arbitrary forcing function. For instance, the lesson uses the example of an earthquake loading to illustrate these concepts.

Video Highlights

Explanation of the response due to impulse - 0:58
Derivation of the response for the mass spring dashpot system - 1:37
Solution for the complimentary function - 3:00
Explanation of the initial conditions and how to derive the constants - 3:41
Discussion on the response due to a unit force acting on the structure - 4:51
Explanation of the Heaviside step function - 9:27
Derivation of the response due to a block loading - 10:35
Explanation of the impulse response function - 21:13
Derivation of the impulse response function - 28:46
Explanation of how to find the response due to an arbitrary forcing function - 35:57

Key Takeaways:

- The impulse response function is used to determine the response of a system to an impulse.
- The response of a system to arbitrary loading can be calculated using the impulse response function.
- The convolution integral is a mathematical tool used to calculate the total response of a system to an arbitrary forcing function.
- The impulse response function can be derived from the initial response of a system.
- The impulse response function is particularly useful in situations where the forcing function is arbitrary, such as in the case of an earthquake loading.