I missed that it's (kx * x)/2Hooke's Law is a physical principle that states the force required to extend or compress a spring is directly proportional to the distance it is stretched or compressed. This relationship is represented by the equation F = -kx, where F is the force, k is the spring constant, and x is the displacement.
The spring constant, also known as the force constant, is a measure of the stiffness of a spring. It is represented by the letter k and is measured in units of newtons per meter (N/m). A higher spring constant indicates a stiffer spring, meaning it requires more force to stretch or compress it.
The integral is used to calculate the work done by a variable force, such as the force required to stretch or compress a spring. In the context of Hooke's Law, the integral of the force-displacement equation (F = -kx) is used to calculate the potential energy stored in a spring.
The negative sign in the equation F = -kx indicates that the force and displacement are in opposite directions. This means that when the spring is stretched, the force is directed towards the equilibrium position, and when the spring is compressed, the force is directed away from the equilibrium position. This is known as the restoring force, as the spring always wants to return to its equilibrium state.
Hooke's Law has various applications in everyday life, such as in car suspension systems, door hinges, and pogo sticks. It is also used in engineering and construction to determine the appropriate size and strength of springs in various structures and machines.