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Spring Constant Formula

Spring Constant or force constant is defined as the applied force if the displacement in the spring is unity. It is denoted by k.

Consider a force F stretches the spring so that it displaces the equilibrium position by x.

The Spring Constant Formula is given by

Where,
F = Force applied,
x = displacement by the spring

Spring Constant formula is used to find the force applied, displacement and spring constant. It is expressed in Newton per meter (N/m).

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Spring Constant Problems

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Below are  problems based on spring constant which may be useful for you.

Solved Examples

Question 1: A spring with load 2 Kg is stretched by 50 cm. Calculate its spring constant?
Solution:
 
Given: Mass m = 2 Kg,
          Displacement x = 50 cm,
          Force F = m a = 2 Kg $\times$ 0.5 m = 1 N
The spring constant is given by
k = - $\frac{F}{x}$ = - $\frac{1}{0.5}$ = - 2 N/m.
 

Question 2: A girl weighing 30 pounds stretches a spring by 60 cm. Calculate the spring constant of the spring?
Solution:
 
Given: Mass m = 30 lbs = $\frac{30}{2.2}$ = 13.64 Kg.
          Displacement x = 60 cm
The force F = ma = 13.64 $\times$ 9.8 = 133.67 N
The spring constant is given by k = - $\frac{F}{x}$
                                                = - $\frac{133.67}{0.6}$
                                                = - 222.786 N/m.
 

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