Application of lagrangian equations

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Just a question on interpretation of lagrangian equations. If I have derived the equations of motion for a system and the equations are in terms of position of x and acceleration of x, am i able to find the acceleration of the system (acceleration of x) if I have a value for the position (x)?
 
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You'd have to solve the equations of motion and then impose the value you have as boundary condition.

If you need help solving the differential equation, you'll have to give us some more info.