Classical Action for Harmonic Oscillator

1. Sep 2, 2008

DeclanTKatt

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