To insure a point of stable equilibrium, the necessary and sufficient conditions on the potential energy of a physical system, U = U(x), are that dU/dx = 0. What does the second derivative at that point have to be?© BrainMass Inc. brainmass.com October 10, 2019, 7:43 am ad1c9bdddf
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For the equilibrium to be stable the point must be a minima of the potential energy.
A minima point means that the second derivative is POSITIVE.
Think about it as a valley or a dip in the potential energy curve. The force is ...
The solution explains what the sign of the second derivative should be for a system to be in a stable equilibrium