College Physics II – Mechanics, Sound, Oscillations, and Waves
Definition
A stable equilibrium point is a position where an object, when slightly displaced, experiences a net force or torque directed towards that position, causing it to return to equilibrium. In simple harmonic motion, this corresponds to the lowest potential energy configuration.
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At a stable equilibrium point, the potential energy is at a local minimum.
When displaced from a stable equilibrium point, the restoring force acts in the opposite direction of displacement.
In simple harmonic oscillators like springs and pendulums, the stable equilibrium point is where the system naturally comes to rest.
Mathematically, small displacements around a stable equilibrium can be described by Hooke's Law: $F = -kx$.
The frequency of oscillation around a stable equilibrium point is determined by the mass and the stiffness (spring constant) of the system.
Review Questions
What characterizes a stable equilibrium point in terms of potential energy?
How does the restoring force behave when an object is displaced from its stable equilibrium position?
Provide an example of a physical system that has a stable equilibrium point and describe it.
Related terms
Potential Energy: The energy stored in an object due to its position relative to other objects or forces.
Restoring Force: A force that acts to bring an object back to its equilibrium position.
Simple Harmonic Motion: Type of periodic motion where the restoring force is directly proportional to displacement and acts in the direction opposite to that displacement.