Differential Equations Worksheet 2 Math 5A Winter 2010, TA Grace Kennedy Summary: Differential Equations Worksheet 2 Math 5A Winter 2010, TA Grace Kennedy NAME: Course Website: http://www.math.ucsb.edu/yjshu/5aw10/ Section Website: http://math.ucsb.edu/kgracekennedy/W105A.html Supplemental Reading: Farlow's DE and LA (your textbook) Sections 4.1-4.2 2nd order, Linear, Homogeneous DE's with Constant Coefficients Goal : Construct a DE that models the motion of a spring with no external forces and then solve it, making sure to check our solution. Understand how to solve second order, linear homogeneous DE's with constant coefficients and real roots (distinct or repeated) to the characteristic polynomial. Problem 1. In your physics lab, you have a 1 2 kilogram box sitting on a rough surface and hooked to a completely relaxed spring mounted to a wall on the left. When testing the spring's strength, you measured that for every meter you pull the string out, it pulls back with a force of 3 Newtons. You also measured the dampening force of the non-frictionless surface to be 5 Newtons for every 2 meters per second. A small child walks by and gives the box a whack that sends it off towards the wall at a velocity of 1m/s. Let x(t) represent the distance of the box to the right of the end of the spring in a Collections: Mathematics