I have been stuck at this particular problem for a while.This is a problem from Nonlinear Dynamics And Chaos by Strogatz.
The thing I am having hard time finding a mechanical system following dx/dt=sinx even approximately. No, simple harmonic motion doesn't work.
Then, the problem asks to intuitively explain why x=0 and x=pi are stable and unstable fixed points respectively. So, it seems like the system would be 'familiar'.But, I am not finding any 'familiar' system of this equation of motion.
Any hints, please?