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: For what value of d is the frequency of small oscillations largest?

  1. Dec 13, 2006 #1
    1. The problem statement, all variables and given/known data
    A coin of radius R is pivoted at a point that is distance d from the center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest?



    2. Relevant equations

    Frequency = 1/T = (1/2(pi))(k/m)^1/2

    x = A cos( (omega)(t) + phi )



    3. The attempt at a solution

    I assume I have to find some derivative in order to maximize the value, just don't know where to start.
     
  2. jcsd
  3. Dec 13, 2006 #2
    Add on:

    Would this be correct?

    F = ma in the tangental direction

    -mg sin(theta) = ma

    -mg sin(theta) = m((R+d) theta '' ) (note theta '' is 2nd derivative)

    thus omega = (g/(R+d))^1/2

    Or is this totally the wrong idea?
     
  4. Dec 14, 2006 #3

    Meir Achuz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You have to use the moment of inertia of a disk, and then use the parallel axis theorem so that you can apply torque=I alpha to the coin.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook