Lagrangian linear masses (CM)

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Homework Statement


A combination of masses along the z-axis is separated by a distance 'a' with middle mass at origin. The potential is
[tex] V = \frac{1}{2}kx^2 [/tex].
What is the force of constraint using Lagrange multiplier?

Homework Equations


[tex] L = T - V + \lambda f[/tex]


The Attempt at a Solution


I found L and calculated the lagrange eqn of motions but still I am getting
[tex] m \ddot{z} - \lambda = 0 [/tex]

z is not moving, so [tex] \ddot{z} = 0 [/tex].
Based on this [tex] \lambda = 0 [/tex]
Is the question wrong?
 
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Answers and Replies

  • #2
kreil
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You should get 3 equations of motion, one for each coordinate (x,y,z)
 

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