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 firstorder 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 firstorder linear differential equation
y(t) + 5 (dy(t) / dt)
= x(t)
a.
Compute the zeroinput response (general solution of the homogeneous equation) to
find the systemspecific part of the response (output) e
λ
t
.
b.
Compute the unitstep 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 timebase t = 0:0.02:50.
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 Fall '08
 JANOS
 Derivative, 0.02 sec, Dr. K. Wage

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