Control Systems Stability

7) Stability of system. 8) What is gain margin and systen bandwidth. 9) Determine y(t). 10) System poles in LHP.
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.... We'll have:

Then, we rationalize the equation:

Then we'll get the Nyquist frequency that crosses the real plane, meaning, imaginary part is zero at that point. So:

Now that the Nyquist frequency at the real part is obtained, we can calculate the real part:

Now, we'll get the gain margin by:

To get the gain margin in dB, we'll use:

Answer: Gm = -1.16dB

Using ...