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## Homework Statement

Calculate the Lagrangian of this set up:

Imagine having two ropes: They are both attached to the ceiling and have different lengths. One has length b and the other has length 4b. Say they are hooked to the ceiling a distance 4b apart. Now, the ropes are both hooked to a plank of mass M (uniform mass density) of length 5b. The rod can move in 3 dimensions. Ultimately, I am after the normal frequencies and normal modes of the system, but I think I can determine these if I can figure out this lagrangian

## Homework Equations

[tex] \mathcal{L} = T-U [/tex]

## The Attempt at a Solution

Well, Im not entirely sure how to go about this but my book suggests to use the coordinate [itex] x [/itex] for the longitudinal displacement of the rod and [itex] y_1[/itex] and [itex] y_2[/itex] as the sideways displacement of the rods two ends. Also, we are only assuming small displacements from equilibrium (so I think [itex] \dot{z} [/itex] is going to be zero)

Im not sure how to implement this choice of generalized coordinates.

Can anyone help me out? Also, I have never found a lagrangian for an extended object (its always been point masses in various systems)

Thanks in advance - btw I cannot find ANYTHING online that resembles a problem like this.