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Unformatted text preview: Uniﬁed Engineering II Spring 2004 Problem S4 (Signals and Systems)
Note: This problem is similar to one given a couple years ago. Please try to do this
one without looking at bibles — the solution is instructive.
One of the beneﬁts of the approach of using the superposition integral is that
you don’t have to guess the particular solution — it pops right out of the integral,
automatically. In some cases, the particular solution can be hard to guess, but easy
to ﬁnd using the convolution integral. To see this, consider the system described by
the diﬀerential equation
d2
d
y (t) + 5 y (t) + 6y (t) = u(t)
2
dt
dt
1. Find the step response of the system.
2. Take the derivative of the step response to ﬁnd the impulse response.
3. Now assume that the input is given by
u(t) = e−2t σ (t)
Before doing part (4), try to ﬁnd the particular solution by the usual method,
that is, by intelligent guessing. Be careful — it may not be what you expect!
4. Now ﬁnd y (t) using the superposition integral. Is the particular solution what
you expected? ...
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This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
 Fall '05
 MarkDrela

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