Bar and spring oscillation problem

1. The problem statement, all variables and given/known data

A bar with length [itex]l[/itex] and homogeneous mass distribution (mass: [itex]m[/itex]) can rotate around its fixed point [itex]O[/itex].The other edge of the bar is connected to the spring in the figure of constant [itex]k[/itex] and length [itex]l[/itex], and the spring is fixed by its one edge at point [itex]P[/itex]. The system is in the homogeneous gravitational field of the Earth.

i)find the positions of equilibrium (stable and unstable)
ii)show that for a small [itex]\widehat{\theta}[/itex] the motion that will result is approximately harmonic oscillation.

2. Relevant equations

[itex]kl = mg[/itex]

3. The attempt at a solution
First of all, the only equilibrium must be the stable one with θ=0rad since kl=mg.

I tried calculating the Δx (in the length of the spring) using simple triangle geometry but the result is very messy and doesn’t get me anywhere.

This is not like any other oscillation problem I have encountered so pardon my ignorance.

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