MAE107L  Dynamic Systems Laboratory
Fall 2009
Lab Report #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.
where the Fourier series coefficients associated with u(t), y1(t), and y2(t) can be
calculated as follows
Since we sample the signals, though, they must be passed through an antialias filter to
remove those frequencies outside of the Nyquist band [−ωN,ωN], where ωN = 1/2ts.
The periodic, continuoustime, 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 determine the Fourier series
components of the original continuoustime signal within the Nyquist band. The
fft command in Matlab computes the discretetime Fourier series coefficients of a
periodic sequence of samples.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Methods
Sinusoidal Input
An interesting aspect of the bottom disk frequency response is a notch located near 4
Hz. Any input at this frequency will result in little to no movement of the bottom disk. The
middle disk acts as a vibration absorber for the bottom disk at a frequency very near the
resonance of the original 1 degree of freedom system. By adjusting the frequency of a
sinusoidal input to the system we have located the precise location of the notch and
measured the rotation of both the middle and lower disks.
Experiments
In the experiment, three different input signals are applied to the torsional system: a
short pulse, a long pulse, and a sawtooth function. The parameters of the inputs are as
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '06
 TSAO
 Fourier Series, Torsion, 1 degree, Dynamic Systems Laboratory, middle disk

Click to edit the document details