1. The problem statement, all variables and given/known data Includes picture, download question "http://docs.google.com/Doc?id=ajccwmhrc3rx_37gs2ht7g9" [Broken]. 2. Relevant equations The potential energy equation ends up being [tex]V = 1/2 k x^2 + W y[/tex] 3. The attempt at a solution xspring = 2 sin([tex]\Theta[/tex]) ym = 2 cos([tex]\Theta[/tex]) [tex]V = 1/2*40 (2 * sin(\Theta))^2 + 7 * 2 * g cos \Theta[/tex] [tex]dV/d\Theta = 160sin(\Theta)cos(\Theta)-14g*sin(\Theta) = 0[/tex] Solving returns theta = 0, 0.5404057 rad (31 degrees) That sounds about right, so now I look for stability [tex]d^2V/d\Theta^2 = 160cos(\Theta)^2-160sin(\Theta)^2-14g*cos(\Theta)[/tex] This is where I'm stuck. Using intuition, I feel the system should be UNstable at theta = 0 and find stability at theta = 31 degrees. Solving the second derivative, I get [tex]d^2V/d\Theta^2(0) > 0[/tex] and [tex]d^2V/d\Theta^2(.54) < 0[/tex] Is the math wrong or is my understanding of stability wrong?