# Classical Action for Harmonic Oscillator

by DeclanTKatt
Tags: action, classical, harmonic, oscillator
 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 Euler-Lagrange equations. 2. Relevant equations The Lagrangian for such an oscillator is L=(1/2)m($$\dot{x}$$2-$$\omega$$2x2) This is easy enough to solve for. The classical action is defined by Scl=$$\int$$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($$\omega$$t) $$\dot{x}$$=$$\omega$$cos($$\omega$$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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