Spring Constant Formula

According to Hooke’s law, the force required to compress or extend a spring is directly proportional to the distance it is stretched.

Spring Constant Formula

The formula of spring constant is given as:

Formula F=-kx
SI unit N.m-1

Where,

  • F is the restoring force of the spring directed towards the equilibrium
  • k is the spring constant in N.m-1
  • x is the displacement of the spring from its equilibrium position

In other words, the spring constant is the force applied if the displacement in the spring is unity. If a force F is considered that stretches the spring so that it displaces the equilibrium position by x.

Spring Constant Dimensional Formula

We know that,

F=-kx

Therefore, \(k=\frac{F}{x}\)

Dimension of F=[MLT-2]

Dimension of x= [L]

Therefore, dimension of k=\(k=\frac{[MLT^{-2}]}{[L]}=[MT^{-2}]\)

Spring Constant

The Spring Constant Formula is given as, \(k=\frac{F}{x}\) where,

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

It is expressed in Newton per meter (N/m).

Solved Examples

Example 1 A spring with load 5 Kg is stretched by 40 cm. Determine its spring constant.
Solution:
Given:
Mass m = 5 Kg

Displacement x = 40 cm

We know that,

Force F = m a = 5 × 0.4 = 2 N

The spring constant is given as:
\(k=\frac{F}{x}\)

= – 2 / 0.4= – 5 N/m

Example 2 A boy weighing 20 pounds stretches a spring by 50 cm. Determine the spring constant of the spring.
Solution:
Given:
Mass m = 20 lbs = 20 / 2.2 = 9.09 Kg

Displacement x = 50 cm

The force F = ma = 9.09 × 9.8 = 89.082 N

The spring constant formula is given by:
\(k=\frac{F}{x}\)

= – 89.082 / 0.5 = – 178.164 N/m.

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