ECE 493
HW #0 –
Version 1.00 January 19, 2011
Spring 2011
Univ. of Illinois
Due Thu, Jan. 25
Prof. Allen
Topic of this homework:
Evaluation exercises; Not graded.
Deliverables:
You best attempt at the questions. If you don’t know, just say so. I’m looking for
your collective baseline. It is not in your best interest to answer questions you don’t understand
(e.g., don’t copy stuff from Wikipedia).
1.
(a) Integrate the equation
F
=
ma
where
F
is the force, acceler
ation
a
=
dv/dt
is the rate
of change of the velocity
v
(
t
),
and
m
is the mass.
Solution:
F
(
t
) =
m
dv
dt
it follows that
integraldisplay
dv
=
1
m
integraldisplay
F
(
t
)
dt.
Justify the above procedures and clean up the argument.
(b) If
F
(
t
) =
δ
(
t
) then the velocity is a step function at t=0
v
(
t
) =
1
m
integraldisplay
δ
(
t
)
/mdt
=
u
(
t
)
.
(c) What is the displacement
x
(
t
) if
v
≡
dx/dt
?
(d) What if
F
(
t
) = sin(
cx

t
)? Find
∂F
∂x
=?
2. Given the differential equation ¨
x
+
b
(
x
) ˙
x
+ 1 = 0
(a) What is the order
(b) If
b
(
x
) = 0, the equation homogeneous or inhomogeneous?
Explain.
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 Spring '11
 JontB.Allen
 Fourier Series, Alternating Current, Complex number, Electrical impedance

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