I solved this by seeing that x has to equal y in the 2 equations, so I got a new equation with $$2\ddot{x}+\frac{g}{r}x=0$$ which was the generic harmonic equation I was looking for.
Hey, I solved a problem about a double pendulum and got 2 euler-lagrange equations:
1) x''+y''+g/r*x=0
2) x''+y'' +g/r*y=0 (where x is actually a tetha and y=phi)
the '' stand for the 2nd derivation after t, so you can see the basic harmonic oscillator equation with a term x'' or y'' that...