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DeclanTKatt
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Homework Statement
Hello. I am attempting to evaluate the classical action of a harmonic oscillator by using the Euler-Lagrange equations.
Homework Equations
The Lagrangian for such an oscillator is
$$ L=(1/2)m(\dot{x}^2-\omega^2 x^2) $$
This is easy enough to solve for. The classical action is defined by $$ S_{cl} = \int L dt$$
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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