sp_S8_mud

# sp_S8_mud - Lecture S8 Muddiest Points General Comments...

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Lecture S8 Muddiest Points General Comments Today, we did a little review of Laplace transforms, and saw how to use them in the analysis of systems. The most confusion seems to be about the region of convergence. Responses to Muddiest-Part-of-the-Lecture Cards (17 cards) 1. You always want us to out the region of convergence, but what does it mean to at σ ( t converge or not converge? (1 student) Consider the LT of g ( t ) = e ). The LT integral is given by G ( s ) = e at e st dt = e ( a s ) t dt 0 0 As t , the integrand either goes to zero or goes to inFnity, depending on whether a s is negative or positive. If a s is negative, the integrand goes to zero exponentially fast, which means the integral is Fnite (there is Fnite are under the graph of e ( a s ) t ), so we say the integral converges. if a s is positive, the integrand blows up, so the integral is inFnite — it doesn’t converge. So the LT is only well-deFned for s > a . 2.

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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_S8_mud - Lecture S8 Muddiest Points General Comments...

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