Lagrangian linear masses (CM) (1 Viewer)

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1. The problem statement, all variables and given/known data
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?

2. Relevant equations
[tex] L = T - V + \lambda f[/tex]

3. 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?
Last edited:


Insights Author
Gold Member
You should get 3 equations of motion, one for each coordinate (x,y,z)

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