A force directed opposite the displacement of a mass from some equilibrium position that acts to restore the mass to the equilibrium location. The most commonly analyzed case is a restoring force which has a magnitude linearly proportional to the displacement from equilibrium, leading to Simple Harmonic Motion.
Utility of the Linear Approximation
The mathematics of Taylor series expansions can be used to show that the motion of any system subject to a net restoring force will be accurately described by the Simple Harmonic Motion model for very small displacements from equilibrium.
As with any series expansion, the term "very small" must be defined for a given system according to the parameters of the relevant force law and the desired accuracy of the description.
2 Comments
Anonymous
In the most familiar case, often referred to as Hooke's Law, the displacement of the system from it's equilibrium position determines the momentary strength of the restoring force, given by
F(x)=- k(x-x_eq).
The negative sign accounts for the direction of the force to restore the system to equilibrium and the constant "k" is the physical parameter that determines the relative strength of the force in terms of the measured displacement dimensions.
Anonymous
In the most familiar case, often referred to as Hooke's Law, the displacement of the system from it's equilibrium position determines the momentary strength of the restoring force, given by
F(x)=- k(x-x_eq).
The negative sign accounts for the direction of the force to restore the system to equilibrium and the constant "k" is the physical parameter that determines the relative strength of the force in terms of the measured displacement dimensions.