1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

DE: Critical Damping Oscillating?

  1. Apr 22, 2014 #1
    I'm having a problem understanding a critical damping model. I know critical damping is supposed to return the system to equilibrium as quickly as possible without oscillating, and a critically damped system will have repeated roots so the general solution will be: c1e^rt + c2te^rt

    But what happens when c2 is negative, for instance when solving y''+6y'+9y=0, y(pi)=-(pi-2)e^(-3pi), y'(pi)=(3pi-7)e^(-3pi), the characteristic equation is r^2 +6r +9, r =-3 repeated, then solving for the initial conditions I get: c1=2, c2=-1, then:

    y(t)=2e^(-3t) -te^(-3t)

    This function drops quickly to 0 at t=2, but then it crosses the origin. I thought it wasn't supposed to oscillate since it's critically damped? I've never taken a physics class so I think I must be missing some physical intuition or something here. Any help is appreciated, thanks.
     
  2. jcsd
  3. Apr 23, 2014 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You're not missing anything. Oscillation means it will cross the t-axis repeatedly. If the system crosses just once, it's not oscillating.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: DE: Critical Damping Oscillating?
Loading...