A particle is under the action of a central forceF.(r,$\displaystyle \theta$) are polar coordinates in the plane of action so that $\displaystyle \textbf{F}=F(r) \textbf{e}_r$. I need to find F(r) given that $\displaystyle r(\theta)=\frac{a}{\sinh(\omega \theta)}$.

So $\displaystyle \ddot{r}-r\dot{\theta}^2=F(r)$ and the transverse component of the acceleration is 0.

Can someone help me solve the above using the definition of r to find F(r)?

Thanks in advance.