Question

(1 point) Math 216 Homework webHW10, Problem 8 Consider the spring model " – 182 +2:03 = 0, where the linear part of the spring is repulsive rather than attractive (for a normal spring it is attractive). Rewrite this as a system of first-order equations in 2 and y=r'. x' = y' = Write down your system when you have it correct, for use in the next three problems. Then find all critical points and enter them below, in order of increasing x coordinate. (x, y) = ( ): (x,y) = ( ): (x,y) = ( : For reference for the next three problems, write down your critical points after you've gotten them all right.

Answer 1

Given equation is, x" – 18x+2x = 0 .(1) Let x = x y = x' Differentiate these, we get (since x' = y) y' = x" = 18x- 2x (by (1)) x' = x' = y Therefore, x' = y y'= 18x- 2x To find the crtical points, solve x' = 0,y' = 0 =y = 0, 18x – 2x = 0 =9x-x = 0 =x(9-x*) = 0 =x = 0,3,-3 Therefore the critical points are (0,0),(3,0), (-3,0)