## Spring Constant Formula :

The spring constant formula F_{(N)} in Newton and equal to minus of the spring constant -k _{(Nm-1 )} in Newton meter^{-1} and multiply the object displacement of the spring from its equilibrium position x _{(Nm)} in Newton meter. Hence the spring constant formula can be written as

**F _{(N)}=-k _{(Nm-1 )}*x _{(Nm)}**

Where,

SI unit Nm^{-1}

F → restoring force of the spring directed toward the equilibrium in Newton

K → spring constant in Nm^{-1}

X → displacement of the spring from its equilibrium position Nm

## Sample Problems :

### Example 1 :

Calculate the spring constant? In a spring with load 5Kg is stretched by 80cm.

### Solution :

Given,

Mass m=5Kg

Displacement x=80cm

We know that

Force F =ma=5×0.8=4N

The spring constant is given as

K=-F/x

=-4/0.8=-5N

### Example 2 :

Calculate the spring constant of the spring? In a boy weighing 20 pounds stretches a spring by 80cm.

### Solution :

Given,

Mass m=20Ibs=20/2.2=9.09kg

Displacement=80cm

The force F=ma=9×9.8=89.082N

The spring constant formula is given by

K=-F/x

=-89.082/0.8=-111.3525N/m