Lagrangian Mechanics with one constraint

[Natchanon]

Homework Statement

I'm supposed to find the normal force acting on the box by the slab as a function of time. The problem is I don't know what the constraint is. I can't find the relation between r and theta that adds the two up to zero.

Homework Equations

Lagrangian equation.

The Attempt at a Solution

I tried constraint f(r, theta , t) = theta and got lamda = mr (gcos(theta) + r theta(double dot) ) = mgrcos(theta) since omega is constant, but still couldn't get the right answer.

 

[TSny]

Hello, and welcome to PF.

If you know $r$ and $\theta$ as functions of time, then I don't understand why you would need to bother with setting up the Lagrangian. Did you state the problem word-for-word as given to you?

 

[Natchanon]

Hello, and welcome to PF.

If you know $r$ and $\theta$ as functions of time, then I don't understand why you would need to bother with setting up the Lagrangian. Did you state the problem word-for-word as given to you?

Sorry for the late reply. I was able to figure it out. Thank you.