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Assignment 4-Questions

Assignment 4-Questions - ECE3085 Homework#1 Due Jan 4 2009...

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ECE3085 - Homework #1 Due: Jan. 4, 2009 Problem 1. (8 pts) Write the dynamic equations describing the circuit in Figure 1(a), where L = 1 H , R = 2Ω , and C = 1 F , with the initial conditions y (0) = 2 V and ˙ y (0) = 1 V . In particular, (a) Write them as a second order differential equation where V out is the measurement y and V in is the input u . (b) Transform the differential equation into the Laplace domain. (c) Assuming a zero input, solve the differential equation for y ( t ) using Laplace transform methods. (d) Verify your answer numerically, by modifying the differential equation from Homework 1, Problem 6b (as I did in the solutions to the last homework). Problem 2. (6 pts) Using Matlab’s roots command determine the poles, associated modes, and stability type for the following transfer functions: (a) G ( s ) = 1 s 3 +2 s 2 +21 s - 58 , (b) G ( s ) = s - 1 s 3 +11 s 2 +39 s +29 , and (c) G ( s ) = 1 s 4 +5 s 3 +11 s 2 +22 s +10 . Problem 3. (10 pts) You are given the circuit shown in figure 1(b). (a) Using the impedance method and the voltage division rule, determine the transfer function G ( s ) for the circuit, where V in is the input and V out is the measurement.

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