HW7 - EEL 3105 Fall 2011 Homework 7 1. Consider the 2nd...

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Unformatted text preview: EEL 3105 Fall 2011 Homework 7 1. Consider the 2nd order differential equation d2y dy dy k 16 y 0, y (0) 1, (0) 0 2 dt dt dt Find solution y(t) for the following values of k: k=12, k=6, k=5.6, k=2, k=0, k=‐1. Choose a suitable time interval and plot these solutions. You can use MATLAB or some other computational math tool for plotting y(t). Comment on your answers. 2. Consider the differential equation d2y dy 5.6 16 y r (t ) 2 dt dt Find impulse response of this system. In other words, find y(t) for r(t) = unit impulse function and initial conditions y(0)=0 and dy (0) 0. dt 3. Consider the differential equation d3y d2y dy 5 2 7 10 y u (t ) 3 dt dt dt Set this up as a state‐space linear system of the form dx(t ) Ax(t ) Bu (t ) dt y (t ) Cx(t ) Find suitable matrices A, B, and C. What are the eigenvalues of A? Is this system stable? ...
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This note was uploaded on 12/27/2011 for the course EEL 3105 taught by Professor Boykins during the Fall '10 term at University of Florida.

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