## Spring Force Formula :

The spring force F_{(N/M)} in newton per meter is equal to the product of the spring constant k_{(N/M) }in newton per meter is multiply by the displacement of the spring from its position at equilibrium x is subtracted by the equilibrium position x_{o }.hence the spring force formula has been written as,

**F _{(N/M)} = k_{(N/M) }(x – x_{0})**

Where,

F → spring force (N/M)

x_{o } → equilibrium position

x → displacement of the spring from its position at equilibrium

k → spring constant (N/M)

The negative sign tells that the visualized spring force is a restoring force and acts in the opposite direction.

## Sample Sums :

### Sum1 :

Calculate its spring constant? in a spring has length 20 cm/s. If it is loaded with 2 kg, it gets stretched by 10 cm/s.

### Solution :

We have,

m = 2

x = 20

x_{o} = 10

Calculate the spring force.

F = ma

= 2 (20 – 10)

= 2 (10)

= 20 N

Using the formula for spring constant we get,

k = – F/(x – x_{o})

= – 20/(20 – 10)

= – 20/10

= -2 N/m.

### Sum2 :

Calculate its spring constant? If a body is stretched by 3m with force 300 N.

### Solution:

Known:

(Displacement) x = 2m

(force) F = 100 N

The spring constant is articulated as,

K = – F /x

K = – 300 N/ 3m

K = -100 N/m.