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220-P3 - ECE 220 Signals and Systems I Fall 2007 Laboratory...

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ECE 220 Signals and Systems I Fall 2007 Laboratory Project 3 Report due: Oct. 20 The purpose of this exercise is to study the behavior of first-order dynamic systems and the solution of the differential equation describing them. Also to introduce you to the MATLAB function lsim , serving for the simulation of linear systems. (Simulation is basically the numerical computation of the system output in response to a specified input.) 1. Hand calculations Consider the first-order linear differential equation y(t) + 5 (dy(t) / dt) = x(t) a. Compute the zero-input response (general solution of the homogeneous equation) to find the system-specific part of the response (output) e λ t . b. Compute the unit-step response, that is, the response when x 1 (t) = u(t), y(t) t=0 = 0. Call this response y 1 (t). c. Compute the response to x 2 (t) = sin(0.2 π t) u(t), with y(t) t=0 = 0. Call this response y 2 (t). Express y 2 (t) as K 1 e λ t + K 2 cos( ϖ t+ ϕ ). 2. Plotting and analysis Plot the two responses, y 1 (t) and y 2 (t), in separate plots, against a time-base t = 0:0.02:50.
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