18.03 Lecture Notes - Lecture 11: System Of Linear Equations, Dashpot, Physical Model
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[1] second order equations are the basis of analysis of mechanical and electrical systems. A spring is attached to a wall and a cart: spring mass. Set up the coordinate system so that at x = 0 the spring is relaxed, which means that it is exerting no force. In addition to the spring, suppose that there is another force acting on the cart -- an "external force," maybe wind blowing on a sail attached to it, maybe gravity, or some other force. The spring force is characterized by the fact that it depends only on position. I sketched a graph of f_spr(x) as a function of x . The simplest way to model this behavior (and one which is valid in general for small x , by the tangent line approximation) is. F_spr(x) = -kx k > 0 the "spring constant. " This is another example of the linear approximation that linn was discussing on monday.
