What is typically measured to determine the stiffness of a spring?

The stiffness of a spring is quantitatively described by the spring constant, often denoted as k. The spring constant is a measure of how much force is needed to stretch or compress the spring by a certain distance. According to Hooke's Law, the relationship between the force applied to a spring and the displacement of the spring is linear, meaning that the force exerted by the spring is directly proportional to the distance it is stretched or compressed. Therefore, a higher spring constant indicates a stiffer spring that requires more force to achieve the same displacement compared to a spring with a lower spring constant.

In contrast, other options such as spring energy or frequency do not directly measure stiffness. Spring energy can refer to the potential energy stored in a spring when it is deformed but does not provide a direct measure of stiffness itself. Frequency pertains to oscillations and is related to how a spring-mass system vibrates, but it is also not a direct indicator of spring stiffness. Elastic rate, while it might intuitively seem related, is not a standard term used in physics to quantify spring stiffness. Hence, the spring constant is the correct and conventional measure used to determine how stiff a spring is.