LINEAR SPRINGS

A linear spring is one which obeys Hooke’s Law. Hooke’s Law prescribes a linear relationship between the force exerted by a spring when it is stretched some distance x. Hooke’s law can be represented as

where k is the spring constant. Equation 1↑ applies to a spring both in stretching and in compressing. The negative sign implies that the force exerted by the spring is always in the opposite direction of x. Therefore, the spring always exerts a force which attempts to restore it to its unstretched condition.

The spring constant is also sometimes referred to as the stiffness, and the concept can be applied to many much more complicated systems. See the Applications page for more information.

The potential energy stored in a spring is also related to the stretching length x. Since Eq. 1↑ represents a conservative force, the change in potential energy that occurs when the spring is stretched is equal to the work done by the force  − F (the force  − F is the force applied to the spring, whereas the force F is that applied by the spring, according to Newton’s third law). Therefore, the potential energy stored in a spring with a stretched length is equal to the work required to stretch it from its unstretched length to x, or