A discrete-time LTI system H has input x[n] and output y[n] related by the linear constant coefficient difference equation y[n]
− 1 2 y[n − 1] = x[n] + 1 3 x[n − 1]. (a) Find the transfer function H(z). Note: you can find the functional form of H(z), but in this part you do not yet have enough information to find the ROC. In parts (c) and (e) you will be given more information so that you can find the ROC. (b) Give a pole-zero plot for H(z). (c) Now assume that the system frequency response H(e jω) exists. For this assumption, give the ROC of H(z) and find the system impulse response h[n]. (d) Under the assumption of part (c) – that H(e jω) exists – is the system causal? Is it stable? (e) Now assume that the system H is unstable and is not causal. For these assumptions, give the ROC of H(z) and find the impulse response h[n]
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Answer:
The natural angular frequency of the rod is 53.56 rad/sec
Explanation:
Since the beam is free at one end and fixed at the other hence the beam is a cantilevered beam as shown in the attached figure
We know that when a unit force is placed at the end of a cantilever the displacement of the free end is given by
Hence we can write
Comparing with the standard spring equation we find the cantilever analogous to spring with
Now the angular frequency of a spring is given by
where
'm' is the mass of the load
Thus applying values we get
