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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


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    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.
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