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 !!

Hint:
Any equation of type $y''+a^2y=0$ can be solved by testing $y=e^{rx}$ as a solution which will result in $r^2+a^2=0$. 
$s''+ {\sqrt{\frac{g}{4R}}}^2s =s''+ a^2s=0\implies s=C_1exp(iat)+C_1exp(-iat)\implies s (t) = A \cos \sqrt{ \frac{g}{4R} } t + B \sin \sqrt{ \frac{g}{4R} } t $.
angular-frequency [rad/s] means $a$ in $s''+ a^2s=0$ which is $\sqrt \frac{g}{4R}$. You can check its dimensional also.    
