Classical Action for Harmonic Oscillator

  1. 1. The problem statement, all variables and given/known data
    Hello. I am attempting to evaluate the classical action of a harmonic oscillator by using the Euler-Lagrange equations.

    2. Relevant equations
    The Lagrangian for such an oscillator is

    L=(1/2)m([tex]\dot{x}[/tex]2-[tex]\omega[/tex]2x2)

    This is easy enough to solve for. The classical action is defined by Scl=[tex]\int[/tex]L dt

    3. The attempt at a solution
    I know what the answer is, but I am having difficulty achieving it. So far I have used:
    x=sin([tex]\omega[/tex]t)
    [tex]\dot{x}[/tex]=[tex]\omega[/tex]cos([tex]\omega[/tex]t)

    Substituted these into the Lagrangian and then integrated, with respect to t, for the classical action. This did not provide the proper results.

    Any suggestions would be greatly appreciated. Thanks
     
  2. jcsd
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