# HW4.pdf - The University of Texas at Austin Department of...

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The University of Texas at Austin Department of Electrical and Computer Engineering EE362K: Introduction to Automatic Control Fall, 2019 Problem Set 4 Recommended Reading: Chapters 5 & 6 of Astrom & Murray 1. F or a mass-spring-damper system with m=4, c=.75, and k=6, determine the damping coefficient, natural frequency, and damped frequency for the system. On a single graph, compare the analytical solution presented in class to numerical solution given by ode45( ) if the initial conditions are x (0)= v (0)=1. 2. By hand, find the eigenvalues and eigenvectors for the following matrices. Verify your answers using the eig() function in MATLAB and explain any discrepancies. 3. Analytically (if possible) determine what the equilibrium points are for the system below and which (if any) are stable. Then, using MATLAB, produce a single phase-plane portrait for the following complex system for the initial conditions: [3, 1], [1, 1],[4, -2] and two of your choosing where (if possible) one converges to an equilibrium point and one does not.
• Fall '19

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