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# HW1 - MAE107 Homework#1 Prof M'Closkey Due Date The...

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MAE107 Homework #1 Prof. M’Closkey Due Date The homework is due by 5PM, Thursday, January 15, 2009 to Mr. David Shatto in the 38-137 foyer (3rd ﬂoor Engineering 4). Mandatory Reading Please read the following sections from the course text: 1. All of Chapter 1. This introductory chapter broadly discusses dynamic analysis, block dia- grams and linear differential equations. 2. The introduction to Chapter 2 and the following subsections: 2.1 (don’t worry about the author’s description of through and across variables); 2.6 (the first physical system studied in the lab is an RC circuit so this section provides a good review of modeling such systems). 3. The introduction to “Part B” starting on page 179. 4. The introduction to Chapter 6 and the following subsections: 6.1 through 6.7 (reviews linear, first-order differential equations). Problem 1 Recall the two RC circuit configurations: 1. Low-pass filter configuration: R 1 C 1 + V in + V out The differential equation relating the dependent variable V out to the imposed voltage V in is given by d dt ( V out ( t )) + 1 R 1 C 1 V out ( t ) = 1 R 1 C 1 V in ( t ) , (1) The reason this circuit and its associated differential equation is referred to as a low-pass filter will become clear when we discuss frequency response functions in several weeks. 1

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2. High-pass filter configuration: C 2 R 2 + V in + V out The differential equation relating the dependent variable V out to the imposed voltage V in is given by R 2 C 2 d dt ( V out ( t )) + V out ( t ) = R 2 C 2 d dt ( V in ( t )) . (2) The reason this circuit and its associated differential equation is referred to as a high-pass filter will become clear in several weeks. For this problem derive the relationship between the dependent variable V out and the imposed voltage V in when these two circuits are connected together to form a single as shown circuit: R 1 C 1 C 2 R 2 + V in + V out In other words, the “ V out
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