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  1. Mechanical Stability

    Linked via "restoring force"

    Stable Equilibrium
    A system is in stable equilibrium if, following a small displacement $(\delta x)$, the system experiences a restoring force or torque that attempts to return it to the original position $(x_0)$. Mathematically, this corresponds to a local minimum in the system’s potential energy function, $U(x)$, such that the second derivative is positive:
    $$
    \frac{\partial^2 U}{\partial x^2} > 0 \quad \text{at } x = x_0

  2. Minimum

    Linked via "restoring force"

    Potential Energy Wells
    A physical minimum corresponds to a potential energy well. A particle residing at the absolute minimum of the potential energy function $V(x)$ is in a state of stable equilibrium. If slightly perturbed, the system experiences a restoring force driving it back towards the minimum. This stability is mathematically confirmed when the second derivative of the potential energy is po…