https://electricalstudent.com/15-2-for-the-oscillator-described-in-problem-15-1-find-the-characteristic-equation-and-use-it-to-show-that-independent-of-the-values-of-a-and-k-the-poles-of-the-circuit-lie-at-a-radial-distance-of/
15.2 For the oscillator described in Problem 15.1, find the characteristic equation and use it to show that, independent of the values of A and K, the poles of the circuit lie at a radial distance of ω0. Find the values of AK that results in the poles appearing (a) on the jω axis, and (b) in the right half of the s plane, at a horizontal distance from the jω axis of ω0/(2Q).