Pretty much a pendulum with variyng length based on the angle.
$\frac{d\lambda}{d\theta}(\frac{d\theta}{dt})^2+\lambda *\frac{d^2\theta}{dt^2}+9.8\lambda*\sin\theta=0$
$\lambda(\theta)=a^2+b^2-2ab\sin\theta$
$l=\sqrt\lambda$ (you can make that substitution later if possible).
Conditions:
$a$ and $b$ are constants.
$\sin\theta\approx\theta$ (you can just replace sin with just theta if you want)
$\theta(t):\theta(0)=\theta_0$
${\dot{\theta}}(0)=0$
I really don't have the experience to solve this. If someone could show the answer and some steps along the way that would be much appreciated.
Hint.
We have
$$ \frac{d\lambda}{d\theta}\dot\theta = -2ab\cos\theta\dot\theta $$
then
$$ \frac{d\lambda}{d\theta} = -2ab\cos\theta $$
following the pertinent substitutions.