LAB 4 has a typographical error which ruins everything. In fact, those of you who tried to convince me that there was a minus sign missing were right. The equation should say

Answer questions 1, 2, and 3 of Lab 4.3 in the text. That is, do questions 1 and 2 for the undamped system, then do questions 1 and 2 for a damped system.

Recall that, to analyze the behavior of a system near an equilibrium point, you should compute the Jacobian, evaluate it at the equilibrium point, and study the corresponding linear system. That is, find the type, eigenvalues and eigenvectors of the linear system.

In problem 2, you should discuss each equilibrium solution, and each type of non-equilibrium solution. Your analysis should be analytic. However, to check your results and produce sample phase plots for your report, you should choose parameter values ( a and L ) and initial conditions ( y and v ) corresponding to each case, and observe the results using MATLAB.

Describe the behavior of the physical system, i.e., in terms of the mass and spring. Don't just describe the trajectories in the phase plane, though you should explain the correspondence between the two.

Finally, note that symmetry may allow you to consolidate some cases, allowing you to reduce the number of different cases you have to discuss.