18.03 Lecture Notes - Lecture 14: Dashpot, Wronskian, Linear Algebra
Document Summary
Model oscillatory behavior using 2nd order linear odes. Find exponential solutions for homogeneous, 2nd order, constant coef cient odes. Write general homogeneous solutions as the span of a set of independent homogeneous solution functions. Use the wronskian to determine if pairs of functions that solve 2nd order odes are linear independent. Problem 2. 1: a cart is attached to a spring attached to a wall. The cart is attached also to a dashpot, a damping service. A dashpot could be a cylinder lled with oil that a piston moves through. Door dampers and car shock absorbers often actually work this way. Also, there is an external force acting on the cart. Physics tells us that fspring is a function of x (opposite sign) and fdashpot is a function of x (opposite sign) Carts attached to spring are not necessarily what interest us.
