**Spring Constant Formula**

We are all familiar with the concept of springs. They are commonly found in pens, toys, and other household items.

One of the characteristics that distinguish a spring is its way of retaining its length even after stretching. It simply returns to its original shape, which is fascinating.

When the spring is pulled apart, a force is usually applied to extend the spring in direction opposite the spring’s centre. When something or someone pulls on the spring, tension is created in the spring, causing it to spring back toward the centre of the spring when the stress is released, i.e. when the thing or person holding it lets go. That’s the force calculated by the student using Hooke’s law. The formula of spring constant is an essential component of the simple harmonic motion.

Simple harmonic motion is the repetitive back and forth motion through a central position with the maximum displacement solely on a single side corresponding to the maximum displacement on either side.

Hooke’s law describes the relationship between applied force and distance stretched in a spring. The force needed to compress or extend any spring is proportional to its length.

## Spring Constant Formula

F= -K × x

**Solved Examples**

**1. Find the spring constant for a spring if it requires a 9000 Newton force to pull the spring 30.0 cm from the position of equilibrium.**

To solve for the spring constant, k, we can rearrange the formula for spring constant as:

F= -K × x

i.e. K = −F/x

In this example, a 9000 N force is pulling on a spring. It means that the spring pulls back with an equal and opposite force of -9000 N.

Also, the displacement is 30.0 cm = 0.30 m. Thus, putting the values in the above formula, we get,

K = −90000/.30

i.e. K= 300000 N/m

The spring constant of this spring is 300000 N/m.

**2. A 3500 Newton force is applied to a spring that has a spring constant of k = 14000 N/m. Calculate how far from equilibrium the spring will be displaced?**

We can find the displacement by rearranging the spring constant formula:

F= -K × x

i.e. x = −F/K

In this example, a 3500 N force is pulling on a spring. It means that the spring pulls back with an equal and opposite force of -3500 N.

Thus,

x = −3500/14000

x=0.250 m

x = 25.0 cm

Therefore, the spring is displaced by 25.0 cm.