Classical Action for Harmonic Oscillatorby DeclanTKatt Tags: action, classical, harmonic, oscillator 

#1
Sep208, 12:40 AM

P: 3

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 EulerLagrange equations. 2. Relevant equations The Lagrangian for such an oscillator is L=(1/2)m([tex]\dot{x}[/tex]^{2}[tex]\omega[/tex]^{2}x^{2}) This is easy enough to solve for. The classical action is defined by S_{cl}=[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 


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