Laplace Transforms 8: The complex frequency domain for s
(Video 8 of several) We discuss how the Laplace transform takes us from the time domain to the complex frequency domain. In particular, this transformation converts a differential equation with respect to t into an algebraic equation in terms of the complex frequency s. I mention how I like to justify the form of the Laplace transform: the process is the right way to extract the key natural frequencies associated with solutions to second-order differential equations. We then look at some general examples involving over damped, critically damped, under damped, and undamped spring-mass systems (harmonic oscillators). As we do this, we notice that by setting y(0)=0 and y'(0)=0, we can identify the transfer function H(s). Up next we will work with the Heaviside function!
Part 7: • Laplace Transforms 7: Example with resonan...
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