What Is the Force of Constraint Using Lagrange Multiplier?

[mamou6262]

Homework Statement

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

Homework Equations

$$L = T - V + \lambda f$$

The Attempt at a Solution

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

z is not moving, so $$\ddot{z} = 0$$.
Based on this $$\lambda = 0$$
Is the question wrong?

 

[kreil]

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