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Homework Help: Simple Harmonic Oscillator

  1. Feb 23, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi,

    For a certain oscillator the net force on a body, with mass m, is given by F=-cx^3.

    One quarter of a period is the time taken for the body to move from x=0 to x=A (where A is the amplitude of the oscillation). Calculate this time and hence the period.

    2. Relevant equations

    [tex]U(x)=(cx^4)/4[/tex], where U(x) represents the potential energy of the body.


    3. The attempt at a solution

    In order to solve this I used a homogeneity of units argument as follows,

    Units of time are [tex](s)[/tex]

    Units of potential energy are [tex](kg*m^2)/(s^2)[/tex]

    In order to get from the potential energy units to the time units,

    [tex](s)=\sqrt{((kg*m^2)/(s^2))}[/tex]

    in terms of the above equations this is,

    [tex]\sqrt{(m*x^2/U(x))}[/tex]=[tex]\sqrt{((4*m*x^2)/(c*x^4))}[/tex]

    let x=A and the equation =T/4,

    [tex]T/4=\sqrt{((4*m)/(cA^2))}[/tex]

    hence, [tex]T=4*\sqrt{((4*m)/(cA^2))}[/tex]

    However this is incorrect, my answer is wrong by a multiplicative factor. Please could someone show me where I have gone wrong?
     
    Last edited: Feb 23, 2008
  2. jcsd
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