DeclanTKatt
Sep2-08, 01:40 AM
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-\omega2x2)
This is easy enough to solve for. The classical action is defined by Scl=\intL 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(\omegat)
\dot{x}=\omegacos(\omegat)
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
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-\omega2x2)
This is easy enough to solve for. The classical action is defined by Scl=\intL 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(\omegat)
\dot{x}=\omegacos(\omegat)
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