For each of these problems, do a short write-up discussing the parameters you used and the effect they have on the solutions to the ODEs. Make one Matlab file for each problem. 1.) 2.) 3.) Also determine the response to a periodic function in Problem 2 as well as the Fourier components, and show that the two approaches give the same response. 4.) Using Matlab, study the effects of varying parameters of the system on the step response for underdamped, damped and critically damped systems. Also study the frequency response and determine the response of the system to the periodic input that you chose in Problem 4.
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