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Jan 11, 2024 · STABLE, UNSTABLE AND NEUTRAL EQUILIBRIUM. Stable Equilibrium: A body is in stable equilibrium if it comes back to its normal position on slight displacement. Examples (1) A ball in the valley between two hills. a small displacement of the ball toward either side will result in a force returning the ball to the original position.
Jul 20, 2023 · What is a stable sorting algorithm? A sorting algorithm is said to be stable if two objects with equal keys appear in the same order in sorted output as they appear in the input data set. Formally stability may be defined as, how the algorithm treats equal elements.
Feb 1, 2021 · A stable atmosphere will have largely flat layers of cloud, which may exhibit some lumpiness but will not extend far upwards. There may be several such layers or, occasionally, clear skies. Unstable air will generally have tall cauliflower-like clouds known as cumulus.
A system is in unstable equilibrium if, when displaced from equilibrium, it experiences a net force or torque in the same direction as the displacement from equilibrium. A system is in neutral equilibrium if its equilibrium is independent of displacements from its original position.
The equilibrium solution $y = 1$ is green and is a semi-stable equilibrium solution. The equilibrium solution $y = 2$ is yellow and is an asymptotically stable equilibrium solution. The equilibrium solution $y = 3$ is red and is an unstable equilibrium solution.
Eigenvalues can be used to determine whether a fixed point (also known as an equilibrium point) is stable or unstable. A stable fixed point is such that a system can be initially disturbed around its fixed point yet eventually return to its original location and remain there.
Explicitly, if the potential is concave-up at x 0, \(\mathrm{\frac{d^2U(x)}{dx^2}|_{x_0}>0}\), then the system is stable; conversely, if the potential is concave-down, then the equilibrium is unstable.
