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# HW2 - MAE107 Homework#2 Prof M'Closkey Due Date The...

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MAE107 Homework #2 Prof. M’Closkey Due Date The homework is due by Friday, 5PM, January 23, 2009 to Mr. David Shatto in the 38-137 foyer (3rd ﬂoor Engineering 4). Mandatory Reading Please review the following sections from the course text: 1. Sections 6.8 and 6.10. NOTE: the text’s notation is different from what I use in class: the text often uses the variable x to denote the input to a system; the symbol u in the text is reserved for the unit step function ( u ( t ) = 1 , t 0 and 0 for t < 0) –our notation is μ for the unit step function; in the text, when a function of time is multiplied by the step function u , for example, h ( t ) = e - σt u ( t ) (see equation 6.35 on page 212), what the author wishes to explicitly point out is that h is zero for t < 0. 2. Sections 9.1 (quaintly describes logging data with a strip chart recorder), 9.3 (describes how you can experimentally measure a system’s frequency response function, 9.4 (describes how you can calculate the frequency response from the differential equation), 9.5 and 9.6 (discusses how to graph the frequency response). Problem 1 Consider Problem 6.27 on page 790, course text. Note that this problem is similar to Problem 4 from Homework 1 with exception that the input voltage to the overall system now directly drives the motor amplifier and the output of the system is the voltage across the capacitor of the low-pass filter circuit. 1. Consider the block diagram shown below for this interconnection of systems: Motor amplifier Motor mechanics Tachometer electronics RC network v 1 ( t ) M 4 ( t ) Ω( t ) v 8 ( t ) v 3 ( t ) Fill in the appropriate differential equation in each block with the input and output variables labeled as shown. Note that the op amp circuits effectively isolate each block from its neighbor.

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