Problem with a physical equation When I solved a physics problem, I found a little problem of math calculation at :
$$E=E_{c}+E_{p}= \frac{ms'^2}{2}+ \frac{mgs^2}{8R} ~~~~\text{(1)}$$
(this is the equation where I met the problem for solving it). The problem said that are no neconservative force, so our $E$ will be zero. 
I derivate the equation $\text{(1)}$ and I obtained:
$$s''+ \frac{gs}{4R} =0 ~~~~\text{(2)} $$ 
Now, the problem asks for pulsation. I don't know how to find angular-frequency [rad/s] beginning from the equation $\text{(2)}$. Any help or hint will be receive very well !!

Let $ \theta = \dfrac {s}{R},$ be the angle of pendulum thread with respect to vertical direction.
$$s''+ \frac{gs}{4R} =0 ~~~~\text{(2)} $$ 
$$\theta ''+ \frac{g \theta }{4R} =0 ~~~~\text{(3)} $$ 
This is simple harmonic angular motion in place of the linear motion. (It is a linear vibration model which approximates $\sin\theta $ as $\theta $)
An odd solution is 
$$ \theta = \alpha \sin ( \omega \,\theta) ~~~~\text{(4)} $$ where
$$ \alpha = \theta_{max} ,\omega^2 = \frac{g}{4 R} , \omega = 2 \pi f = \frac{2 \pi}{T}, ~~~~\text{(5)}  $$
where $ T$ is the time period, $f$ is frequency and $\omega$, the angular velocity just as it is with rectilinear motion.
