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!

Homework Help: Critical Damping

  1. Nov 5, 2005 #1
    Show that the equation x(t)=(A+Bt)e^(-Beta*t) is indeed the solution for critical damping by assuming a solution of the form x(t)=y(t)exp(-Beta*t) and determining the function y(t).

    Is there a differential equation for the critically damped case that I can substitute x(t) and its appropriate derivatives into to solve for y(t)?? Hints, please!!! There are no examples like this in the text...
  2. jcsd
  3. Nov 5, 2005 #2


    User Avatar
    Homework Helper

    This is more of a ODE problem than a physics one as you have notice.
    The differential equation for the free damping idealized spring:
    [tex] m \ddot{x} + c \dot{x} + kx = 0 [/tex]
    For the case of critical damping the characteristic polynomial for this linear ODE indicates repeated roots. Well give it a try.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook