Understanding Dynamic Systems Impulse and Frequency Response

This course covers the fundamental concepts of impulse response function, frequency response function, and their applications in dynamic systems. It starts with the response of a system to an impulse and the calculation of the response to arbitrary loading. The course then explains the derivation of the impulse response function and introduces the concept of a convolution integral. For instance, the course uses an earthquake loading scenario to illustrate these concepts. The course also covers the numerical implementation of Duhamel's Integral in MATLAB to solve for the response due to arbitrary loading in a system. Furthermore, the course delves into the concept of frequency response function, the Fourier series, and Fourier transform as mathematical tools for dynamic analysis. Lastly, the course discusses the Fourier series representation and its application in structural dynamic analysis, including the calculation of the coefficients of a Fourier series.