https://www.chenk.top/en/tags/characteristic-equation/Recent content in Characteristic Equation on Chen Kai BlogHugoenFri, 04 Aug 2023 09:00:00 +0000https://www.chenk.top/en/ode/03-linear-theory/Fri, 04 Aug 2023 09:00:00 +0000https://www.chenk.top/en/ode/03-linear-theory/<p><strong>A first-order ODE has memory of one number; a second-order ODE has memory of two.</strong> That tiny extra degree of freedom is what lets the same equation describe a plucked guitar string, the suspension of your car, the L-C tank circuit inside an FM radio, and the swaying of a tall building in the wind. In every case the same three regimes appear — oscillate, return-with-a-touch-of-overshoot, or crawl back — and the same algebraic gadget, the <em>characteristic equation</em>, predicts which one happens.</p>