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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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