- #1
brentd49
- 74
- 0
I will make a crude visualization of this system:
|-------------O--------------|
<-----a------><------a------>
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].
|-------------O--------------|
<-----a------><------a------>
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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