Final answer:
An expression for the stable fixed point is obtained by considering the potential energy curves and finding the point where the force changes from positive to negative.
Step-by-step explanation:
An expression for the stable fixed point can be obtained by considering the potential energy curves. In a stable equilibrium point, the force on one side of the fixed point is positive, while on the other side it is negative. This means that the potential energy at the stable fixed point is at a minimum.
For example, in Figure 15.14, the first condition represents a stable equilibrium point where the force on one side points away from the fixed point, while the second and third conditions represent unstable equilibrium points where the force on only one side points toward the fixed point.
Therefore, an expression for the stable fixed point can be written as the point where the force changes from positive to negative, indicating a minimum in the potential energy curve.