The negative of the slope, on either side of the equilibrium point, gives a force pointing back to the equilibrium point, F = ±kx, so the equilibrium is termed stable and the force is called a restoring force.

There is a deep connection between force and potential energy. This relationship has a useful graphical representation that will help us better understand the spring-mass potential energy and, in Chapter 3, the potential energy associated with the bonding between atoms.

Jan 11, 2024 · For stable equilibrium, the second derivative should be positive. So for slight displacement, the restoring force should act on the body $\frac {d^{2}U}{dx^{2}} > 0$ potential energy diagram for the Stable Equilibrium. For unstable equilibrium, the …

The negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle. At an equilibrium point, the slope is zero and is a stable (unstable) equilibrium for a potential energy minimum (maximum).

We call the point \(x=0\) a “stable equilibrium”, because it is a local minimum of the potential energy function. If the object is displaced from the equilibrium point, it will want to move back towards that point.

Determining whether an equilibrium point in a potential energy versus displacement graph is similar to the illustration above. Let's consider the following plot: Image source: Force and Potential Energy - Physics LibreTexts. The points of equilibrium are where the slope is zero.

The force associated with a potential energy is equal to (-1) times the slope at any position. Consider the graph below. Where does the force equal zero? We call a location where the force on an object is zero an equilibrium point. There are three obvious equilibria in the graph above.

Sketch these three equilibrium configurations, and identify them as positions of stable, unstable, or neutral equilibrium. For the potential energy curve shown in Figure 2, (a) determine whether the force F x is positive, negative, or zero at the five points indicated. (b) Indicate points of stable, unstable, and neutral equilibrium.

The negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle. At an equilibrium point, the slope is zero and is a stable (unstable) equilibrium for a potential energy minimum (maximum).

There are two basic things to know about potential energy diagrams: equilibrium points and accessibility. A local maximum is said to be a point of unstable equilibrium, because an object placed at such a point will not return to its equilibrium position after being displaced slightly.