A thin rod of length 2b is suspended by 2 light strings both attached to the ceiling. Using x, y1, y2 as your generalized coordinates right down the lagrangian of the system. Where x is the longitudinal displacement of the rod and y1 and y2 are the horizontal displacements of the ends.
The strings remain taught and displacements from equilibrium are small
The Attempt at a Solution
If θ Is the angle that one of the strings makes with the vertical and we make a small angle approximation then θ= (x^2 +y^2)/l but and the height above the equilibrium position is equal to l(1-cos θ) which is approximately equal to l(θ^2), but this gives me a bunch of very small terms which I don't think is correct