How do you derive the effective spring constant?

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Answer 1 · 2017-12-25T06:38:08

You can measure it, the spring constant (k) is

# k = F/x #

where F is the force applied to stretch (or compress) a spring,
x is the elongation (or compression) measured after the force is applied.

A) Concept:

The spring constant of a spring is how much a spring will stretch or compress if a force is applied to it.

For example, if 1-N force stretches a spring by 2cm, then its

spring constant# = (1N)/(2cm) = 0.5 N/(cm)= 50 N/m #

50 N/m is the spring constant #-# read: it requires 50 N to stretch the spring by 1.0 m.

It is a constant because If you apply 10-N force, you expect the spring to stretch by 20 cm.

Spring constant = 10N/20 cm = 0.5 N/(cm)= 50 N/m #

If you stretch the same spring by 5 cm, how much force must you use? Since each cm requires 0.5 N, then 5 cm requires 5 x .5N= 2.5 N.

We can formulate this relationship of Force to elongation
# F/x = k# where k is the spring constant

#F = k x #

where F is the force applied in Newton, and x is the elongation (or compression) in meter. If k = 50 N/m,

then # F = 50 x #

The spring force found inside the spring, however, is opposite to the force you applied to it, there the spring force is

# F_("spring") = - kx #

B) Measurement...