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

The response of a circuit or other oscillatory system to an input of frequency ω (“omega”) is described by the function

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50 φ(ω) = @₂ (A) D = 0.01 Both wo (the natural frequency of the system) and D (the damping factor) are positive constants. The graph of ø is called a resonance curve, and the positive frequency w, > 0, where takes its maximum value, if it exists, is called the resonant frequency. Show that w, = √√w² - 2 - 2D² if 0