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**EDIT**: possible approach iff v = (const)/√x. I should have looked at all the prior posts so the following is wheel-spinning ... I don't read Russian but post 40 sure looks like v = 0.55

*something*/s i.e. constant.

1. Let length of pendula = L instead of 1. I don't lke losing the ability to check dimensions as I stumble along.

2. Change v = a/√x to c/√x. "a" should be reserved for acceleration.

So one mass starts at x = -x

_{0}/2 and the other at x = x

_{0}/2.

With these mods, taking the mass at x= x

_{0}/2,

Σ F

_{x}/m = a

_{x}= kq

^{2}(x)/mx

^{2}- gx/2L,

v

_{x}= ∫ a

_{x}dt = ∫ a

_{x}/v

_{x}dx = cx

^{-1/2}

winding up after some grief with

q

^{2}(x) = (m/2k)(gx

^{3}/L - c

^{2})

So we have q(x).

To get q(t) solve dx/dt = -cx

^{-1/2}giving x(t) = {x

_{0}

^{3/2}- (3/2)ct}

^{2/3}.

Then substitute for x in q(x) and that's it.

Still

*very*laborious. Lots of opportunities for mistakes!

I wonder if we could cheat and ignore gravity?

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