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: Particle in Stable/Unstable Motion, Find Frequency of Oscillation

  1. Feb 19, 2010 #1
    1. The problem statement, all variables and given/known data
    A particle moves around the surface of an upside-down cone, in a horizontal circular path, in equilibrium. The particle is given a small radial kick. Use the Lagrangian equation for motion (found in a previous section of this problem):

    m[tex]\ddot{r}[/tex] = (ml[tex]_{z}[/tex][tex]^{2}[/tex])/(r[tex]^{3}[/tex]cos[tex]^{2}[/tex]([tex]\alpha[/tex])sin[tex]^{2}[/tex]([tex]\alpha[/tex])) - cos([tex]\alpha[/tex])mg

    to decide whether the circular path is stable. If so, with what frequency does r oscillate about the equilibrium?

    2. Relevant equations

    3. The attempt at a solution

    If I can put in r[tex]_{o}[/tex] ± [tex]\epsilon[/tex] for r in that equation and show that the right side is positive when epsilon is negative and negative when epsilon is positive, then I will have shown that it is stable.

    But I don't know how to do that. Also, when I can show that it is stable, how should I go about knowing the frequency of oscillation?
  2. jcsd
  3. Feb 19, 2010 #2


    User Avatar
    Homework Helper

    You know that at some value of r, the left side is equal to 0. What happens to the right side if you make r bigger? Does the second derivative of r become negative or positive?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook