I will make a crude visualization of this system:(adsbygoogle = window.adsbygoogle || []).push({});

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Identical springs: k1=k2=k

Natural Length: l > a

The problem is to prove that the system is unstable.

Obviously, a slight movement directed off the horizontal axis will cause the springs to unstretch to a natural position vertically above or below the current position. The setup is arranged on a frictionless horizontal table.

I know that the second derivative of the potential energy will tell me about the stability, so I am trying to write down the potential energy. My problem is how to write down the 'x' for the two springs, i.e.

[tex] U(x) = \frac{1}{2} k x^2_1 + \frac{1}{2} k x^2_2 , x_1=x_2[/tex]

[tex] U(x) = k x^2 [/tex]

I suppose it is just a geometry question, but I'm not sure to find that compressed length [tex]x[/tex].

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# Homework Help: Two Compressed Springs -> Unstable Equilibrium

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