Summary: Differential Equations Worksheet 2
Math 5A Winter 2010, TA Grace Kennedy
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