From: prussing@aae.uiuc.edu (John Prussing) Subject: Re: Physical Solutions Solutions to Qudratic Equations Date: Sat, 21 Oct 2000 00:38:38 GMT Newsgroups: sci.math Summary: [missing] In <8sq365$k2b$1@newsg3.svr.pol.co.uk> "Nick" writes: >I seem to recall hearing years ago that solutions to quadratic equations >could be modelled by using electric/electronic circuits. >Does this ring bells with anybody? Does anybody know of a reference I can >look up (the search engines are useless)? >Thanks >Nick Perhaps you're referring to modeling a second-order linear ODE using an electrical circuit. If one connects a resistor, capacitor, and inductor in a single loop, a homogeneous second-order ODE can be simulated. If one includes a voltage source, an inhomogeneous ODE can be simulated. The voltage-current relationship for each of the elements is different. For the resistor Vr = iR, where Vr is the voltage change across the resistor, i is the current flowing through it, and R is its resistance. For the capacitor i = C*dVc/dt, where C is the capacitance, and for the inductor Vi = L* di/dt, where L is the inductance. For a single-loop RLC circuit the current i is the same through each element and the voltage changes around the loop must sum to zero: Vr + Vc + Vi = 0. With a voltage source V(t) must also be included. Using i as the dependent variable one gets a second-order ODE. The resistance R simulates damping. A mechanical simulation would use a mass, spring, and damper. That's my guess at what you are trying to recall. -- =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-= John E. Prussing Dept. of Aeronautical & Astronautical Engineering University of Illinois at Urbana-Champaign http://www.uiuc.edu/~prussing =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=