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oh hello this morning we'd like to start a discussion of the Dynamics of feedback systems to this point we've been looking at feedback systems where the quantities in the loop in particular the forward path transmission a and the feedback path transmission F have been pure numbers they've been frequency independent and we've concentrated on modeling feedback systems using these quantities and on exploring the important properties associated with the resultant systems in particular what we found out is that if the loop transmission magnitude in particular in particular the AF product is large compared to one then in fact the properties of the system are uniquely determined by the feedback path this is the important property of a feedback system in particular that if we have a large enough Loop transmission magnitude we can virtually uniquely determine the behavior of the system via the feedback path and in particular the closed loop gain of the system is ap...

What we'd like to do is to create a single abstraction that can be used to address all our synchronization needs. In the early 1960's, the Dutch computer scientist Edsger Dijkstra proposed a new abstract data type called the semaphore, which has an integer value greater than or equal to 0. A programmer can declare a semaphore as shown here, specifying its initial value. The semaphore lives in a memory location shared by all the processes that need to synchronize their operation. The semaphore is accessed with two operations: WAIT and SIGNAL. The WAIT operation will wait until the specified semaphore has a value greater than 0, then it will decrement the semaphore value and return to the calling program. If the semaphore value is 0 when WAIT is called, conceptually execution is suspended until the semaphore value is non-zero. In a simple (inefficient) implementation, the WAIT routine loops, periodically testing the value of the semaphore, proceeding when its value ...

Now we'd like to analyze in more depth our result that for a system of particles-- so let's indicate our system. We had particle 1. We have our jth particle. And we have a particle N. So here's our system of particles where the total force caused the momentum of the system of particles to change. Now, I'd like to examine that concept of the total force. Before we said that our total force on the jth particle-- we just wrote it like this. And I'm going to put a little t up here for the moment. Because when we examine what force we mean here-- and I also want to put a little boundary around our system. And let's now consider another particle internal to the system. And let's try to identify the types of forces on the jth particle. We can really have two types of forces here. Our first force can be an interaction between these two particles. So what I'll write is the force on the jth particle due to the interaction between the k and the jth pa...