Hooke’s law

INTRODUCTION:

Robert Hooke, an English scientist first described the mathematical pattern of stretching a spring. It describes the relationship between the force applied to a spring and its resulting displacement.

STATEMENT:

Hooke's law states that:

“The force required to extend or compress a spring by some distance is directly proportional to that distance”.

OR

“Within elastic limit, the displacement produced in the spring is directly proportional to the force applied”.

MATHEMATICAL EXPRESSION:

Consider “$F$” is applied force or load and “$\text {x}$” is the displacement (extension) of spring the the mathematical equation of Hooke’s can be written as:

$F \propto \text{x}$

$\boxed{F=-k\text{x}}$

Here, $k$ is spring constant.

APPLICATION OF HOOKE’S LAW:

Hooke's law is only applicable as long as the spring remains within its elastic limit, beyond which the spring will be permanently deformed.

This law has a wide range of applications, including in the fields of engineering and physics, such as in the design of suspension systems and the measurement of forces in electromechanical devices.