Is the Particle Free? Calculating Equations of Motion

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Homework Statement



The one-dimensional motion of a particle with coordinate q is governed by the Lagrangian

L = (dq/dt)2(6q2 - 4qt(dq/dt) + (dq/dt)2t2)

Show that the particle must be free

Homework Equations





The Attempt at a Solution



I know that L needs to depend only on (dq/dt)2 for the particle to be free, but I don't know how to do it...
 
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One way to show that it is a free particle (i.e., there are no forces on it) is to calculate the equations of motion...if \ddot{q}=0[/itex], then Newton's second law tells you the net force on the particle is everywhere zero.
 

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