(Solution) - Because a center equilibrium is stable but not asymptotically stable -(2025 Original AI-Free Solution)

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Because a center equilibrium is stable but not asymptotically stable, nonlinear perturbation can have different outcomes. shown in Problems I 1 and 12.
1. Determine the stability of the equilibrium solutions of the strong spring i + x + x + x3 = 0.
2. Determine the stability of the equilibrium solutions of the weak spring i + x + x - x3 = 0.