1. In this problem, we'll look at a mass-spring system where the tension on the spring can be adjusted. (a) Write the equation y"+9y' + ky = 0, (k > 0) as a system x' = Ax. (b) Find (T, D) for the matrix A. (c) Find values of k that lead to an underdamped system. What type of equilibrium point corre- sponds to an underdamped system? (d) Find values of k that lead to an overdamped system. What type of equilibrium point corre- sponds to an overdamped system? (e) This equation models a system with friction. Replace the -9 in the matrix A with 0. This corresponds to an undamped system. Show that the equilibrium point corresponding to this system is a center point.

1. In this problem, we'll look at a mass-spring system where the tension on the spring can be adjusted. (a) Write the equation y"+9y' + ky = 0, (k > 0) as a system x' = Ax. (b) Find (T, D) for the matrix A. (c) Find values of k that lead to an underdamped system. What type of equilibrium point corre- sponds to an underdamped system? (d) Find values of k that lead to an overdamped system. What type of equilibrium point corre- sponds to an overdamped system? (e) This equation models a system with friction. Replace the -9 in the matrix A with 0. This corresponds to an undamped system. Show that the equilibrium point corresponding to this system is a center point.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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