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MAE107L Lab 9 Report

MAE107L Lab 9 Report - MAE107L Dynamic Systems Laboratory...

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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 anti-alias filter to remove those frequencies outside of the Nyquist band [−ωN,ωN], where ωN = 1/2ts. The periodic, continuous-time, but band-limited signals, can then be perfectly represented by a periodic sequence of samples. The periodic sequence of samples can be analyzed with discrete-time Fourier series in order to determine the Fourier series components of the original continuous-time signal within the Nyquist band. The fft command in Matlab computes the discrete-time Fourier series coefficients of a periodic sequence of samples.
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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
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MAE107L Lab 9 Report - MAE107L Dynamic Systems Laboratory...

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