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I have been stuck at this particular problem for a while.This is a problem from Nonlinear Dynamics And Chaos by Strogatz. The problem

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?

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It looks like a typo to me: the equation is $\ddot{x}=\sin x$ and this is just a pendulum with a slightly odd convention for the angle. Posit $x = \pi + \theta$ and you get the usual $\ddot{\theta}+\sin\theta = 0$.

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You can consider a pendulum with HUGE friction. In that case you can neglect second derivative and get the required equation.

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There are some fine examples here, for instance:

An inverted pendulum in a very viscous medium.

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  • $\begingroup$ The problem is about finding a mechanical analog! $\endgroup$ – Mockingbird Nov 13 '17 at 3:56
  • $\begingroup$ Sorry I don't have enough reputation to make a comment. But this is possibly duplicated $\endgroup$ – Math The Novice Nov 13 '17 at 4:06
  • $\begingroup$ @MathTheNovice, the duplicates refer to answers at Physics SE. $\endgroup$ – stafusa Nov 13 '17 at 7:51

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