MAE107L  Dynamic Systems Laboratory
Fall 2009
Lab Report Template #9
Introduction
In this lab we have used the frequency domain techniques from previous labs to measure the frequency
response of a two degree of freedom torsional system. The two frequency responses, one from the
system input to each of the two rotational disks, is estimated using the relationship between the Fourier
Series of the input and output signals.
H
1
=
F
(
y
1
(
t
))
F
(
u
(
t
))
H
2
=
F
(
y
2
(
t
))
F
(
u
(
t
))
where the Fourier series coefficients associated with
u
(
t
)
,
y
1
(
t
)
, and
y
2
(
t
)
can be calculated as follows
c
k
=
integraldisplay
T
u
(
t
)
e

jk
ϖ
0
t
dt
(1)
Since we sample the signals, though, they must be passed through an
antialias
filter to remove
those frequencies outside of the Nyquist band
[

ϖ
N
,
ϖ
N
]
, where
ϖ
N
=
1
2
t
s
. The periodic, continuous
time, but bandlimited signals, can then be perfectly represented by a periodic sequence of samples.
The periodic sequence of samples can be analyzed with discretetime Fourier series in order to deter
mine the Fourier series components of the original continuoustime signal within the Nyquist band. The
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 Spring '06
 TSAO
 Fourier Series, Torsion, Pulse Sawtooth

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