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!

Mass Spring Damping Question

  1. May 7, 2014 #1
    1. The problem statement, all variables and given/known data
    Suppose a mass- spring is modeled by x''+ cx'+100x. What should the damping constant c be in order that critical damping occurs?

    2. Relevant equations


    3. The attempt at a solution
    I set the discriminant equal to zero so that there are real repeated roots.
    B^2-4ac=0
    c^2=400.
    c=20 or c=-20.
    The answer should only be c=20. For critical damping, the constant must be positive?
     
  2. jcsd
  3. May 7, 2014 #2

    pasmith

    User Avatar
    Homework Helper

    What is the repeated root? You need it to be negative so that [itex]x[/itex] decays with time, do you not?
     
  4. May 7, 2014 #3

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    For any level of damping, c must be positive.

    If c is negative, you are putting energy into the system, not taking energy out.
     
  5. May 7, 2014 #4

    ChrisVer

    User Avatar
    Gold Member

  6. May 7, 2014 #5

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    An other way to look at it: damping force must be opposite to x', which it is if c is positive:

    x'' = -cx' -100x
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted