sp_S2_mud - Lecture S2 Muddiest Points General Comments...

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Lecture S2 Muddiest Points General Comments Today we talked about Duhamel’s integral, which has the nifty property of giving the response of an LTI system to an arbitrary input, u ( t ), if we know the step response, g s ( t ). I appreciate all the cards I received today. I have one request: please write legibly. I can’t always make out what every card says. Responses to Muddiest-Part-of-the-Lecture Cards (38 cards) 1. Who was Duhamel? (1 student) Jean Marie Constant Duhamel was a French mathematician who studied, among other things, heat diffusion. Heat diffusion problems are examples of LTI systems; Duhamel applied some of the ideas we talked about today to these problems. 2. How do you model something with steps if it’s not always increasing in time? (1) All the math that we did works even if the slope of u ( t ) is sometimes negative. When the slope is negative, the steps are negative (downward), which is not a problem. 3. The method [Duhamel’s integral] seems impractical and requires a great deal of known information. Are there alternate methods? (1) We will be studying Laplace transform methods, which are closely related. I would disagree with you, however, that the method is impractical. It really is quite useful, and many disciplines (heat transfer, unsteady aerodynamics, etc.) use Duhamel’s integral in some form. 4. So then the difficulty comes in modeling the step response accurately? (1) Yes, although this is not always that difficult. The result today says that if you can ±nd the step response, though, you are done — you know everything there is to know about the system. 5. Can y ( t ) be expressed as the following y ( t ) = g s · u (0) σ ( t ) + g s σ ( t τ ) u ( τ ) 0 (1) No. As you’ve written it, g s looks like a constant. It’s not — it’s a function of time.
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.

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sp_S2_mud - Lecture S2 Muddiest Points General Comments...

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