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

Both ω0 (the natural frequency of the system) and D (the damping factor) are positive constants. The graph of ϕ is called a resonance curve, and the positive frequency ωr > 0, where ϕ takes its maximum value, if it exists, is called the resonant frequency. Show that

and that no resonant frequency exists otherwise (Figure 21).

Transcribed Image Text:

φ(w) = (2)2+4D202 D.5 42 (B) D-0.2 FIGURE 21 Resonance curves with al-I. (A) D-0.01 (C)D 0.75 (no resonance)