The response of a circuit or other oscillatory system to an input of frequency (omega)

Chapter 4, Problem 79

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The response of a circuit or other oscillatory system to an input of frequency (omega) is described by the function () = 1 (2 0 2)2 + 4D22 Both 0 (the natural frequency of the system) and D (the damping factor) are positive constants. The graph of is called a resonance curve, and the positive frequency r > 0, where takes its maximum value, if it exists, is called the resonant frequency. Show that r = 2 0 2D2 if 0

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