PROBLEMS TO BE WRITTEN UP AND TURNED IN AT RECITATION These problems are due at your first recitation meeting after Wed 11/21. Each problem should be written on a single sheet of paper (front and back), or if multiple sheets are used, staple them together. For full credit, the work must be neat, with clearly labeled diagrams (no diagrams necessary for these problems, they are purely math problems). The labels must be in BOTH words and symbols. For each part of the problem, you must BRIEFLY explain your strategy in words, as well as neatly showing your physics equations and math, with proper units. G1 and G2: (10 points each) The differential equation for an undriven LRC circuit is (q/C) + R(dq/dt) + L(d^2q/dt^2) = 0 Eq (1) Your task is to show that q(t) = (Q_0)e^(-(alpha)t)cos((omega)t) is a solution of this differential equation, where Q_0, alpha, and omega are constants. G1. Substitution of q(t) in Eq (1) gives terms in sin((omega)t) and terms in cos((omega)t). Show that the sin((omega)t) terms sum to zero if and only if alpha = R/2L. G2. Show that the cos((omega)t) terms sum to zero if and only if omega^2 = omega0^2 - alpha^2 where omega0^2 = 1/LC.